The models tend to be very good about syntax, but this sort of linting will often catch dead code like unused variables or arguments.
You do need to rule-prompt that the agent may need to run pre-commit multiple times to verify the changes worked, or to re-add to the commit. Also, frustratingly, you also need to be explicit that pre-commit might fail and it should fix the errors (otherwise sometimes it'll run and say "I ran pre-commit!") For commits there are some other guardrails, like blanket denying git add <wildcard>.
Claude will sometimes complain via its internal monologue when it fails a ton of linter checks and is forced to write complete docstrings for everything. Sometimes you need to nudge it to not give up, and then it will act excited when the number of errors goes down.