In 2364, this light cruiser was under the command of Captain Paul Rice. In that year, Commander William T. Riker, then-XO of the USS Hood, 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 was sent to Minos on a mission to investigate the disappearance of the Minosians. After the ship reported arriving at the planet, there was no further contact with the Drake. The USS Enterprise-D would investigate the disappearance of the Drake and the Minosians.
In a conversation between a holographic image of Rice and Riker, the former, when stating the top speed of the "Drake", used the present verb tense of "is". This indicated to Riker that, while the crew might probably have been killed, the ship itself was not destroyed. When he asked for its location from Rice, he responded that the ship's location was "classified". (TNG: "The Arsenal of Freedom")