In the recently launched episode S02E04 of Star Trek: Discovery, we learned that
Saru belongs to a species on which General Order One (AKA Prime Directive) is applicable.
Have we seen such Starfleet officers in Star Trek before?
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The prime (pardon my pun) example that I can think of is Mirasta Yale, from the Star Trek: The Next Generation episode "First Contact." The episode itself focused on Commander Riker going undercover on a pre-warp planet known as Malcor III to determine whether or not first contact should be made. He is discovered, and chaos ensues on the planet. Captain Picard meets up with some of Malcorian leaders and they determine that the Federation should stay away from Malcor III (for now). However, astronomer and administrator of a NASA-equivalent Yale decides that she wants to join the crew of the Enterprise, and although the audience doesn't ever see her again, it is likely that she joins Starfleet.
Further research regarding pre-warp civilizations and their interactions with Starfleet reveals, civilizations with some interactions with the Federation, but no member of those groups ever joined Starfleet. However, one technicality emerged from my research: Gillian Taylor from Star Trek IV: The Voyage Home. Although Earth was important in the creation of Starfleet and the Federation, when Captain Kirk and the Enterprise crew visited during the 1980s, interstellar travel was limited to going to the Moon and sending out the occasional probe. One could consider it a pre-warp civilization. Doctor Taylor joined crew of the Enterprise in their journey back to the 23rd century. Upon their arrival, she was assigned to a Federation science vessel due to her knowledge of the newly not-extinct humpback whales.
Saru is the first confirmed such character and it's not unlikely that he's the only one ever considering that few inhabitants of pre-warp cultures would have anything to offer Starfleet. However Ensign Ro comes close in that her people were only acquainted with warp drive by being conquered by the Cardassians and she is a precedent for someone who was not originally a Federation citizen managing to get into Starfleet anyway.