This thread was looking lonely, so I'll add some speculation:
I have a feeling that in 4B, Kara is going to be prohibited from being Supergirl by the DEO (maybe under threat of incarceration?) based on a line or two in the 4B promo the CW released a few weeks ago.
If that's the case, I hope it leads to more scenes like in
Bunker Hill, where Brainy helps Kara do her thing in her civilian form since Alex (as Director) is probably going to be under close watch by Hayley. (Bonus if Hayley asks Alex why Agent Dox is hanging out with her sister so much, and Alex makes up a "They're dating" excuse
.)