Part 91 corporate operators also have "Chief Pilots" ... in my case, our department is two pilots, the CP and myself. We both have the usual flying and aircraft support duties. The CP additionally is responsible for overall operation of the department, budgeting, maintenance scheduling, etc. Basically, think management of the department in addition to flying duties.
At Skywsest and I'm sure at other airlines there are several chief pilots. Depending on the size, each domicile has a chief pilot. Some of the smaller domiciles are covered by the chief of one of the larger ones. They all answer to the main chief pilot in HQ who answers to the Director of Flt. Ops. There are a bunch of other positions in the corporate side of an airline a chief pilot can move into: fleet managers, safety officers, flight standardization, etc.