The remote repo should be configured to run gc as needed after a commit is made. See the documentation of gc.auto in git-gc and git-config man pages.
However, a remote repo shouldn’t need all that much garbage collection, since it will rarely have dangling (unreachable) commits. These usually result from things like branch deletion and rebasing, which typically happen only in local repos.
So gc is needed more for repacking, which is for saving storage space rather than removing actual garbage. The gc.auto variable is sufficient for taking care of this.