。
I'd like the reservations clerk, please.
Literal
Reservations-clerk [object-を] please.
A phone-call staple. お願いします is an extremely versatile polite request — here it means 'could you connect me to / get me X.' 予約係 ('reservations clerk') uses the suffix ~係 (kakari), which marks a role or desk: 案内係 (information desk), 会計係 (cashier), etc. Note how direct the request is despite its politeness — Japanese phone etiquette lets you name the target directly.