The Shuttle Pilot is responsible for flying the various small craft found about a Starbase such as shuttles. Normally the marine personnel responsible for the fighter spacecraft fill this role, but due to the diplomatic role the base plays there may be another individual assigned specifically to this position for ferrying about the various VIPs that decline transporter travel or direct docking for whatever reasons.

An example from Star Trek would be Tom Paris. 

This is a specialist position that normally sees a low level of inclusion in most missions.