Management recruits/selects the Chief Pilot.
In the US the FAA sets minimum standards:
FAR 119.67
(b) To serve as Chief Pilot under Sec. 119.65(a) a person must hold an
airline transport pilot certificate with appropriate ratings for at least one
of the airplanes used in the certificate holder's operation and:
(1) In the case of a person becoming a Chief Pilot for the first time ever,
have at least 3 years experience, within the past 6 years, as pilot in
command of a large airplane operated under part 121 or part 135 of this
chapter, if the certificate holder operates large airplanes. If the
certificate holder uses only small airplanes in its operation, the experience
may be obtained in either large or small airplanes.
(2) In the case of a person with previous experience as a Chief Pilot, have
at least 3 years experience, as pilot in command of a large airplane operated
under part 121 or part 135 of this chapter, if the certificate holder
operates large airplanes. If the certificate holder uses only small airplanes
in its operation, the experience may be obtained in either large or small
airplanes.
His duties generally fall under the category of "good order and discipline", assisting the Director of Operations in carrying out all his regulatory responsibilities, and whatever else management tells him to do.
Generally those airlines who have a Pilot on the BoD have one to represent interests of Line Pilots, not management. For the Chief Pilot to have that seat would be a conflict of interest.