Jeager in The Squire of Gothos.
Jaeger's obviously a science officer, and he does claim to be a scientist instead of a "military man" but I see no indication that he's a research scientist, unless you're going to make the claim that Spock, Jadzia Dax, Samantha Wildman, T'Pol, basically anyone else in Star Trek who were identified as science officers were in fact research scientists.
And before anyone jumps up and down about Jaeger claiming not to be a military man, I would like to point out that context matters. Given in the scene Trelane is pestering him about strategies and tactics, all he's doing is pointing out his specialty is in science as opposed to combat and tactics. Not a claim that Starfleet isn't military, and I doubt that was the intent of the episode's writer.
it seemed lie a vast majority of the field officers were scientist. Picard, Geordi, Data, Crusher just about everyone.
Picard was only a science officer in the alternate timeline in Tapestry. Indeed, the very same episode shows he graduated the Academy straight into the Command department, and we know from numerous references in TNG he was a career pilot to. Geordi was also a pilot with engineering background, remember it was an incident where Picard made a causal reference to a shuttle's maintenance which led to Geordi spending an entire night disassembling the shuttle to figure out what was wrong that led to him being noticed by Picard. Data wears gold suggesting he has an engineering background. Dr. Crusher is a medical officer.
Chain of Command-- A fleet of Cardassian ships are caught hiding in a Nebulae. They probably want to invade the nearby system. Captain Jerico wants to confront them. The crew acts really reluctant, suggesting they might be there for scientific research. Crusher seems annoyed that she has to get Sickbay ready in case of casualties.
That scene made it look like a crew of scientists that signed up for organization that sometimes have to do some military service, but they really hate the idea of doing anything militarily related.
To be honest, Chain of Command makes the entire TNG crew look like a bunch of whiners. At the very least, Dr. Crusher's annoyance over getting sickbay ready for casualties is absolutely wrong. Let's not even look at this as a military or not military argument for a moment. A starship on active duty in either unexplored space or the border of a hostile species should have sickbay ready for casualties 24/7 simply because you never know when shit is going to go down, especially a ship with a crew of over 1000, there's plenty of potential for a tragic accident to happen even under routine situations, like in Cause and Effect when Geordi got dizzy and nearly fell down the entire warp core chamber. If making sure sickbay is ready for casualties is such an inconvenience for Crusher, she really should be re-thinking her career.
Besides, considering the same storyline shows Starfleet special ops missions, I'm interested how that somehow fits with the "not a military" line of thinking.