The USS Drake was a Federation light cruiser that was in service with Starfleet in the mid-24th century. In 2364, the Drake was under the command of Captain Paul Rice.
In that year, Commander William T. Riker, then-XO of the USS Enterprise-D, declined Starfleet's offer to take command of the Drake. Riker's classmate at Starfleet Academy, Paul Rice, would later take up the offer to command this starship.
Later that year, the Drake and her crew were destroyed by an automated weapons platform known as the Echo Papa 607 while in orbit of Minos.
The Echo Papa 607, masquerading as Captain Rice, claimed the Drake's top speed as warp three. (TNG: "The Arsenal of Freedom")
According to the Star Trek Encyclopedia (2nd ed., p. 122) this vessel was a Wambundu-class starship, with the registry NCC-20381. The Encyclopedia further notes that the ship was named after Sir Francis Drake.