The hierarchy on board a Private Jet works slightly different than in Airline.
The concept is the same though, but the roles are a bit dissimilar. Depends a lot if the Operator is Aircraft Management or a Charter-Operation based organisation.
On board the Private Jet, of course we have Captain and First Officer.
Sometimes, due to operational needs, there might be two Captains flying together, and the boss is the pilot seated on the left seat. They swap seats every sector or every other day.
In general, on top of that there is the Lead Pilot. He/she is the leader of the team for a specific aircraft.
Then, we have the Fleet Manager. He/she is on top of all lead pilots of all the aircraft of the same fleet.
Going higher there is the Manager of Flight Operations. You may find this also with the acronym “NPFO”: nominated person flight operation. At the top of the scale, the CEO.
Additionally, there are other Managers who work in collaboration with all the components of the hierarchy.
Some examples are Training Manager, Safety and Security Manager, Type Rating Instructor, Type Rating Examiner.
Notice also that the Lead Pilot and Fleet Manager technically don’t have a legal responsibility but is more a leadership and crew management duty.
That’s why in some cases the communication will be between the Captain and the Manager of Flight Operation and CEO.
This happen especially when the event or the decision involve the safety of the Customer, Crew and Jet.
If we talk about heavy jets, or all other Private Jets with single flight attendant operations, then every flight attendant of the whole fleet will refer to the Flight Attendant Manager.
She/he will also actively collaborate with the cockpit hierarchy.
If we talk about airliners, where the crew in the cabin vary from 2 to 5 (depends on the configuration), then one of them is the Lead Flight Attendant and she/he will be on charge of the rest of the team.
She/he will report to the lead pilot and the flight attendant manager.
Again, this is more a managerial/leadership duty.
The Lead Flight Attendant is a team leader, but not necessarily an instructor.
There will be dedicated roles for specific people who will support new joiners during their familiarisation and training.
Same trainers or external resources will be used also for audits.