Curious, do you mean: if a task was part of project ABC, with an ID of ABC-123, then if someone moved it into project DEF, its ID is now changed to DEF-621, those two should be linked, right?
Our Github integration is a two-way sync, so that you can import any open GitHub issues into Tara as Tara tasks. If you update the corresponding the Tara task, the corresponding GitHub issues are also updated, so you can certainly keep using the GitHub issues.
The main benefit of using Tara is that it provides the team a much better way of plan upcoming sprints, and the system also pulls in GitHub PRs to eliminate any blindspots on PRs getting stale.
I'd encourage you to give it a go and try it out to see if it works with your teams workflows.