Update the master branch, which you need to do regardless.
Then, one of:
Rebase the old branch against the master branch. Solve the merge conflicts during rebase, and the result will be an up-to-date branch that merges cleanly against master.
Merge your branch into master, and resolve the merge conflicts.
Merge master into your branch, and resolve the merge conflicts. Then, merging from your branch into master should be clean.
None of these is better than the other, they just have different trade-off patterns.
I would use the rebase approach, which gives cleaner overall results to later readers, in my opinion, but that is nothing aside from personal taste.
To rebase and keep the branch you would:
git checkout <branch> && git rebase <target>
In your case, check out the old branch, then
git rebase master
to get it rebuilt against master.