How to "fork" from a remote branch which becomes HEAD

A remote repository TR has a branch A and I want (without using “Fork”) pull this branch in my local repository B which is an old “Fork” of TR and to start all my futur commits from this A.

A Fork can be done once and i do not want to close this Forked repository. I just want to update my repo and restart from the A branch.

Thank you

You can add the remote repository to the list of remotes of your local repository (git remote add), fetch its current state (git fetch NAME), and then check out the branch you want to track as usual. From there you can make patches, push to your own public repository, and so on.