The USS Prokofiev was a Federation starship that was in service during the late 24th century.
The Prokofiev was dispatched to the border of the Cardassian Demilitarized Zone in late 2370, following the arrest of Starfleet officer Miles O'Brien. The Enterprise-D and the Valdemar were also ordered to patrol the border of the DMZ. (DS9: "Tribunal")
Background
The Star Trek Encyclopedia states that this vessel was an Andromeda-class starship, with a registry of NCC-68814.
The Prokofiev was presumably named after Sergei Prokofiev, a Ukrainian-born Russian composer of the early 20th century.