A Saab 340 pilot reported an engine failure on initial climb out; resulting in return to departure airport and a single engine approach and landing.

Narrative

I experienced an inflight emergency that resulted in an engine shutdown and single engine landing. The flight was operated in a Saab 340. I served as the SIC and Pilot Not Flying. With me was Person A; who served as PIC and Pilot Flying.Conditions at the field were VMC. Tower cleared us to departed on Runway XXL; left turn to heading 120 and climb to 17;000. After passing 400 AGL; we initiated the left turn with no issues. At 1000 AGL; we were handed over to Departure and initiated the climb checklist. During the reduction in power for climb; we experienced symptoms for a right engine compressor stall. Memory items were immediately applied; but were unsuccessful and resulted in the engine failing. I then [requested priority handling] with Departure; and ran our emergency quick reference handbook. Departure cleared us to land back on XXL; and we were able to do so without further issue.Upon exiting Runway XXL at Taxiway 1; Ground Ops did an inspection of our aircraft and saw no signs of damage. We were then cleared to taxi to the FBO; and secured the aircraft without further issues.