ongoing integration of two git repos for a single project

Disclaimer: I understand Git, but am a novice with using it firsthand (managed teams that use it, but have only used it a handful of times).

I created a git repo when I joined current company and have been doing server deployments using git from local using separate branches to deploy to dev/stage/prod. This is all working as expected.

Our creative agency has been working with my company much longer than me (they designed and developed the theme, custom plugins, etc. for the site). They recently started doing some new work and informed me that they have their own repository (logically, they want to retain their repo for historical purposes).

My question: Is there a way that I can integrate their repo with mine? Maybe by deploying commits made to their master branch into a branch in my repo (e.g. dev, stage or feature branches)?

One flaw I see with this approach is how to handle getting my repos changes back to their repo. Is there a way I could manage that? Or is this a lost cause?

Everything I've searched references merging two repos, but I'd like to know if there's a way to keep both working separately.