Don't Jetstar have Fleet managers who report to the Chief Pilot?
The current Qantas Chief Pilot is an occasional A-380 Captain and, from memory, has never flown the 744 or A-330. Does that matter?
The previous Qantas Chief Pilot did not fly anything for about 4 years before he relinquished the position.
It seems to me the Chief Pilot's role is largely regulatory these days and it's up to the individual Fleet Manager and his/her administrative staff to keep track of the specific issues relating to any one fleet.