Secure is a flat adverb (and a sentence adverb) here, meaning securely or assuredly. You can read the sentence as:

Assuredly, it has the ring of a saner sanity than an ordinary discipline and habits of life, than an ordinary organization.

You can derive this by looking at both an adjective and adverb definition of secure and the adverb definition of securely:

secure, adj., adv., and n.1
A. adj. II. That is certain; fully assured; (objectively) safe.
B. adv. In a secure manner; securely, safely; easily.

securely, adv.
3. Without risk of error; with certainty.

Source: Oxford English Dictionary (login required)

By the way, secure as a noun means secure people considered as a class, like the rich and the poor.

Answer from Tinfoil Hat on Stack Exchange
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Merriam-Webster
merriam-webster.com › dictionary › secure
SECURE Definition & Meaning - Merriam-Webster
The meaning of SECURE is free from danger. How to use secure in a sentence. Synonym Discussion of Secure.
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Dictionary.com
dictionary.com › browse › secure
SECURE Definition & Meaning | Dictionary.com
SECURE definition: free from or not exposed to danger or harm; safe. See examples of secure used in a sentence.
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Collins Dictionary
collinsdictionary.com › us › dictionary › english › secure
SECURE definition in American English | Collins English Dictionary
Ensure that the frame is securely fixed to the ground with bolts. ... If you describe something such as a job as secure, it is certain not to change or end.
Published   December 20, 2017
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Encyclopedia Britannica
britannica.com › dictionary › secure
Secure Definition & Meaning | Britannica Dictionary
I was secure in the belief/knowledge that I had done all I could. [=I felt confident because I believed/knew that I had done all I could] They are financially secure. [=they have enough money to live on; they do not have to worry about money] ...
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Merriam-Webster
merriam-webster.com › sentences › secure
Examples of 'SECURE' in a Sentence | Merriam-Webster
Example Sentences secure · adjective · verb · 1 of 2 adjective · Definition of secure · Synonyms for secure · The children were safe and secure in their beds. You should store your valuables in a secure place.
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Sentence Dictionary
sentencedict.com › secure.html
Secure in a sentence (esp. good sentence like quote, proverb...)
free from danger or risk 3. kept safe or defended from danger or injury or loss 4. not likely to fail or give way 5. able to withstand attack 6. financially sound. ... 21 She finished the match,[sentencedict.com] secure in the knowledge that she was through to the next round.
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YourDictionary
sentence.yourdictionary.com › home › secure
Examples of "Secure" in a Sentence | YourDictionary.com
It makes me feel secure to know you're there and I can depend on you. ... She felt secure knowing that he was in charge.
Top answer
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Secure is a flat adverb (and a sentence adverb) here, meaning securely or assuredly. You can read the sentence as:

Assuredly, it has the ring of a saner sanity than an ordinary discipline and habits of life, than an ordinary organization.

You can derive this by looking at both an adjective and adverb definition of secure and the adverb definition of securely:

secure, adj., adv., and n.1
A. adj. II. That is certain; fully assured; (objectively) safe.
B. adv. In a secure manner; securely, safely; easily.

securely, adv.
3. Without risk of error; with certainty.

Source: Oxford English Dictionary (login required)

By the way, secure as a noun means secure people considered as a class, like the rich and the poor.

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The sanity referred to here is secure:

I have no respect for the penetration of any man who can read the report of that conversation, and still call the principal in it insane. It has the ring of a saner sanity than an ordinary discipline and habits of life, than an ordinary organization, secure.

=

It has the ring of a sanity

saner than an ordinary discipline and habits of life,

saner than an ordinary organization,

secure.

=

It has the ring of a secure sanity,

saner than an ordinary discipline and habits of life,

saner than an ordinary organization.

Left to the end for emphasis, and a contrast to the rather long comparative strings that come between it and sanity.

There is no reason to analyze it as a noun as it could not take any dependents typical of one such as determiners (no, a, my) or adjectives (good, sure, possible).

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Justia
dictionary.justia.com › secure
secure Definition, Meaning & Usage | Justia Legal Dictionary
Definitions of "secure" The act of safeguarding from the risk of losing or not obtaining · The process of guaranteeing or assuring a claim, often through a surety · The action of giving assurance for a loan or making certain a payment, execution or performance with a collateral · The practice of providing or promising collateral to a person or entity to whom money is owed How to use "secure" in a sentence ·
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WORDS IN A SENTENCE
wordsinasentence.com › secure-in-a-sentence
Secure: In a Sentence – WORDS IN A SENTENCE
February 22, 2019 - Definition of Secure · to attach something soundly · Examples of Secure in a sentence · Forgetting to secure his bike with the chain, the boy was extremely disappointed to find that it was stolen overnight. 🔊 · Using a kit to secure furniture to the wall is an expensive way to prevent ...
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Cambridge Dictionary
dictionary.cambridge.org › example › english › secure
SECURE in a sentence | Sentence examples by Cambridge Dictionary
In doing so, he secured essentially maritime objectives by diplomatic means. ... Such arrangements are thought to provide the best means of securing members' interests.
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Vocabulary.com
vocabulary.com › dictionary › secure
Secure - Definition, Meaning & Synonyms | Vocabulary.com
Secure means safe, protected. Your money is secure in a bank. Supportive friends and family make you feel secure.
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Cambridge Dictionary
dictionary.cambridge.org › us › dictionary › english › secure
SECURE | definition in the Cambridge English Dictionary
SECURE meaning: 1. positioned or fixed firmly and correctly and therefore not likely to move, fall, or break: 2…. Learn more.
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Bab.la
en.bab.la › sentences › english › secure
secure example sentences - Use secure in a sentence
English The schools must be open and healthcare must be secure. volume_up more_vert ... English We would like to secure two things in this regard.
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Merriam-Webster
merriam-webster.com › dictionary › security
SECURITY Definition & Meaning - Merriam-Webster
The meaning of SECURITY is the quality or state of being secure. How to use security in a sentence.
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Oxford Learner's Dictionaries
oxfordlearnersdictionaries.com › definition › english › secure_2
secure adjective - Definition, pictures, pronunciation and usage notes | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com
Look up any word in the dictionary offline, anytime, anywhere with the Oxford Advanced Learner’s Dictionary app. where somebody/something cannot be harmed; that cannot be affected or harmed by something synonym safe (4) It's important to keep your documents secure.
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Collins Dictionary
collinsdictionary.com › sentences › english › secure
Examples of 'SECURE' in a sentence | Collins English Sentences
No one entered the building because the front and back doors were secure. ... We were made to feel secure in who we were.
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Oxford Learner's Dictionaries
oxfordlearnersdictionaries.com › definition › american_english › secure_2
secure verb - Definition, pictures, pronunciation and usage notes | Oxford Advanced American Dictionary at OxfordLearnersDictionaries.com
3to protect something so that it is safe and difficult to attack or damage secure something against something to secure a property against intruders secure something The windows were secured with locks and bars.
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Reverso
dictionary.reverso.net › english-definition › secure
SECURE - Definition & Meaning - Reverso English Dictionary
secure definition: make certain or guarantee. Check meanings, examples, usage tips, pronunciation, domains, and related words. Discover expressions like "secure tenancy", "secure unit", "secure the deal".
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Longman
ldoceonline.com › dictionary › secure
secure | meaning of secure in Longman Dictionary of Contemporary English | LDOCE
Redgrave won his third Olympic gold medal, and secured his place in history.2 safe from harm to make something safe from being attacked, harmed, or lost Troops were sent to secure the border.secure something against somebody/something They built a ten-foot high fence to secure the house against ...