Merging non-git releases of a project

Here's my dilemma.... I've used git extensively to track modifications
made to a reasonably large source tree. I do not have access to the
repository for that project, just a given release. I have now acquired
the latest version of that project and I want to 'merge' (not sure
that's the right word in this case) my changes into the new version.
Then I need to carry on using git for further changes. I think it
should be simple but I can't get my head around the best way to do
this.

Any pointers appreciated!