In JIRA connected with STASH you can create a feature branch for an issue using the button 'create branch'. (That is nice to track the commits in this issue.)
If a developer started working but did not know that there is such an issue he did not click the 'create branch'.
Is there any possibility to assign an existing git branch to an issue?
ex-Stash developer here.
Yes and no. Creating the branch though the UI is just a convenience. The important thing is that the name contains the JIRA key. If only one developer is working on the branch, it's fairly easy to just rename (delete + add) a branch with the appropriate name.
git checkout old-branch
git push -u origin old-branch:JIRAKEY-1234-something
git push origin :old-branch
Does that help?