The other answers do a great job explaining how to merge branches once you pull or fetch them from the remote. They all assume that your branches have matching names in both repositories, but this is not required by Git.
To have a local branch "back" pull from and push to a remote branch "front", you just need to set up the tracking properly:
git checkout -b back origin/front
will create a new local branch "back" that will pull from remote "front". You can also set up an existing local branch with
git branch --set-upstream-to=origin/front back
The last argument is not necessary if you currently have "back" checked out. See https://stackoverflow.com/a/2286030/2988730 for lots more information on setting up your branches.