Dash 8 Captain reported during initial climb the pitch trim control was stuck in an aft pitch up condition. The flight crew gained manual control of the aircraft and continued to destination airport where they executed a safe landing.

Narrative

Just after acceleration height and after gear and flaps were up; somewhere around 200 kts. we got master caution pitch trim light. Ran the checklist during climb and came to the conclusion we lost pitch trim control meaning the trim was stuck in an aft pitch up condition. Once we leveled off at cruise alt we concluded that 200 kts. was the best airspeed since at that airspeed the aircraft was pretty much trimmed out with very little manual elevator control needed. Called Maintenance and Dispatch and made the decision to continue to ZZZ1. Our biggest concern was how much manual elevator control was going to be needed at landing configuration and which flap setting was going to require the least manual input. Ended up [requesting priority handling] because by asking for XXL it triggered ATC to declare it for us due to priority handling. Landed on XXL with flaps 15 which turned out to be the best configuration since the approach and landing turned out to be a none event. No FAR's or aircraft limitations were exceeded or broken during event.