I might use String#matches() here, with a regex alternation:

CopyString input = "cpr1210";
if (input.matches("(?i).*(?:cpr|cvr|nr).*")) {
    System.out.println("MATCH");
}

If you really wanted to use String#contains(), then you would need to have three separate calls to that method, for each sequence.

I propose the following, null-safe alternative:

Optional.ofNullable(fullString)
  .orElse("")
  .contains(testStr);

Ideone.com demo

When fullStr is in fact null then "" will be used, and .contains(...) will almost always¹ evaluate to false.

If we want to always return false when fullStr is null, we can use:

Optional.ofNullable(fullString)
  .map(s -> s.contains(testStr))
  .orElse(false);

Ideone.com demo

Note that this solution will return false when both fullString and testStr are null. I know that testStr is guaranteed to be != null, but thought it might be worth mentioning.

¹It will evaluate to true when testStr is "" as well