Git remote/shared pre-commit hook

I don't think so, as hooks are not cloned.
May be if that hook script is itself versioned, and then link to (symbolic link) in the clone servers (provided their OS support that link feature).

Or maybe if the hooks are part of a git template directory used for creating the clones (that would only ensure their presences in the clone repo, that would not guarantee they are actually used and executed).

But I don't think there is any "central" way to enforce a commit.

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As Jefromi explains even more clearly in the comments (emphasis mine):

I think it really goes against the idea of a git repository to have enforced hooks distributed with the repo.
My clone is my repository. I should be able to use git on it however I like, including choosing whether or not to run hooks.
(And from a security standpoint, that'd be really kind of scary - no one should have the ability to force me to execute certain scripts whenever I run certain git commands.)

I agree with that comment, and have only seen ways to enforce rules applied locally, in a given specialized repo.
For instance, you wouldn't push to the central repo directly, but would first push to a QA repo which would accept your commit only if it follows certain rules. If it does, then the QA repo will push your commit to the central repo.

Another illustration directly derived from what I just mentioned would be "Serverless Continuous Integration with Git", a way to enforce locally private build that works before pushing them anywhere.

You can not have the pre-commit hook forced on peoples local repositories, but in your central repo you can still run a pre-receive hook.

F. ex I needed to be sure the commit messages obeyed certain rules (for trac integration etc) so I used following pre-receive hook, which checks every commit messages being pushed to the central repository, and will deny the push if it is not welformed.

#!/bin/sh
while read rev_old rev_new ref
do
    MALFORMED="$(git rev-list --oneline $rev_old..$rev_new | egrep -v '#[0-9]+' |  awk '{print $1}' )"
    if [ x"$MALFORMED" != x ]
    then
        echo Invallid commit message on $MALFORMED
        exit 1
    fi
done

for more info see f.ex https://git-scm.com/book/en/v2/Customizing-Git-Git-Hooks

Two options:

1. Use Husky

If you are writing JavaScript, the best way to do this is with Husky. Husky has a postInstall script that will set up and manage your githooks. You can then configure precommit and prepush scripts in your package.json or a husky dotfile.

You can use this to run arbitrary scripts. I typically yarn lint and yarn test prepush.

2. Set core/hooksPath in git.config, then include /hooks in your repo

If you are not using JavaScript, or you cannot use Husky, you can clone commit hooks onto developer machines and check them into a repo, but you cannot force developers to run them.

To check in your hooks, create a hooks directory somewhere in your repo. Then put your hooks there instead of the usual .git/hooks directory. This is the part you can enforce.

The other part depends on developer goodwill. To set your hooks folder as the hooksPath, each developer must run:

git config core.hooksPath hooks

Now all the hooks in the hooks folder will run as you would expect.