OK, I think I understood the question now - and the answer is No.
The 3 regent actions represent a combination of regent/domain effort. Anything that would add a bonus would require some sort of supportive action (adventure), either taken by AAs or the regent (using either a normal regent action or the bonus regent action or the lt bonus action).
As for the description of the action you can describe your regent as taking a personal hand in actions - or not - it depends on your play style I suppose. Its just fluff though, and doesn't given any extra bonus (beyond the possible +2 bonus for a good description).
* Normally a successful supportive adventure gives a +2 bonus to another domain action; very skilled/very lucky AAs can give a bigger bonus +4 or even +6 (very rare). It is also possible to just plain fail if you're low-level or lack appropriate skills, or fail and provide a penalty.