One nice solution to this problem is to use pipx. pipx essentially provides a middle ground between installing nothing to the global python installation and installing everything to the global python installation. pipx is installed into the global python installation and then you use pipx to (1) install (and manage) python-based command line tools (such as pre-commit) within isolated virtual environments and (2) expose those command line tools to the global terminal command namespace. The workflow in this case is:

1. python -m pip install --user pipx to install pipx to the global python.
2. pipx ensurepath to make sure path is setup correctly.
3. pipx install pre-commit
4. pre-commit install in the git repo of interest
5. set up .pre-commit-config.yaml in the git repo of interest
6. Now git commands should work using pre-commit (which uses the pre-commit installed by pipx) on the repo of interest, whether or not the virtual environment is activated.

pre-commit installs isolated environments for each of the tools such that they don't interfere with local development. It sounds like you're missing dependencies in that environment

Running pip install inside the cache environments is very not supported and you are likely to break pre-commit by doing that. They are intentionally private implementation detail so you don't mess with them!

You have two main options:

making your scripts work in isolation (the supported way)

set up your tools such that they specify their dependencies properly (you haven't shown your configuration, but my guess is you're calling some script?)

for repositories that get installed, the dependencies of your tool should be listed in your setup metadata (usually setup.py / setup.cfg / pyproject.toml)

For example, pre-commit/pre-commit-hooks specifies these dependencies:

# setup.cfg
install_requires =
    ruamel.yaml>=0.15
    toml

for local repositories with language: python, you should specify your dependencies in additional_dependencies -- for example:

-   repo: local
    hooks:
    -   id: run-the-thing
        name: run the thing
        entry: ./scripts/lint
        additional_dependencies: [six, ...]
        language: python
        types: [python]

repository local hooks (the escape hatch)

with language: system / language: script, pre-commit does not provision an environment. it is the responsibility of each user to set up such an environment. these are the escape hatch from the normal way because they kind of defeat the purpose of the framework in the first place (which is to provision the tools necessary on its own -- without every developer needing to carefully manage a bunch of tools)

For repo: local you'd use language: system and just hope your script produces a useful error message if the user's environment is misconfigured

-   repo: local
    hooks:
    -   id: run-the-thing
        name: run the thing
        entry: ./scripts/lint
        language: system
        types: [python]

disclaimer: I created pre-commit