... relationship between a Chief and a Divo/DH, etc. ....
The list is long. My pet peeves.
Good order and discipline. Never ever tolerate from the Chief the denigration of anyone in the CoC. The same for sailors that work for him. Keep the realtionship professional. He(she) is not your friend, rather mutual respect is the relationship.
You are always the boss. The new ensign is still in charge of the salty E-9. The Chief is the technial expert, should know a lot about leadership and such as well. I would never (seldom) second guess a Chief on a technical matter in his domain, but all else is yours. Disagreements always in private but do not tolerate "power plays" in front of the sailors.
Do not let the Chief hide out in the CPO mess. He should be with the sailors as much as possible.
Suggest an invite for yourself to the CPO mess for a cup of coffee, he might decline, I never did (refuse). Never invite the Chief to the WardRoom.
This is a little tricky. Always have your ears up and alert to the grapevine. Talk to the sailors directly, individually or in groups, about most any subject. Let them know you are interested in them but never ever try to be their friend. Ever. At all times let them know you have complete confidence in the Chiefs, even if you do not. Know the star performers as well as the slackers that try to game the system.
The CPO is not above the rules, he obeys them like everyone else. Insist on it (in private)
Do not let issues simmer. Take care of them immediately.
Just my .02c. Others may diagree.