What are the researchers required to promote troops to tier 7?

First you will need to have your training camp(s) up to at least level 19 to unlock the tier 7 troops.

For research: Under basic combat you need to research Fighter promotion 1, Shooter promotion 1 and vehicle promotion 1 to allow any of those level 1-3 troops to be promoted to the highest level you have unlocked.

Then in the same section research Fighter Promotion 2, Shooter promotion 2 and vehicle promotion 2 further down to allow level 4-6 troops to be promoted to level 7

If you want to promote level 7 and above troops to higher levels then you need to follow the individual Training research stems (eg Fighter Training) and work your way down to the Promotion 3 item that is near the bottom of each one.