Star Trek Social Club

SNW S1E2 - Children of the Comet. This is a tricky one because of potential predestination and the end result being an accidental major break of the prime directive. A warp capable civilization is certain that a comet must destroy a pre warp civilization and refuse to let that change. The issue is that the ship/comet wants the Federation to interfere and does not intend to hit the planet. This is all in Federation space.

Another in Federation space that is also a loose fit is LD S5E7 - Fully Dialated where the crew must recover Data's head from an alternate reality that has fallen on a pre warp world. The loose fit here is that the only reason they count as external is that it is Purple Data who is not technically a a member of this realities Federation and thus an outsider.

Lastly a decent fit but outside Federation space is Prodigy S1E7 - First Con-Tact. The crew first breaks the prime directive by making first contact with a pre warp civilization but then defends it by stopping a Ferengi from influence the civilization negatively. This is outside Federation space though.

I always felt that they only mentioned the Prime Directive when they were going to violate it

In Star Trek: Insurrection, the Enterprise protected the Baku from the So'na, though if I remember right, there was some debate as to whether the prime directive applied as the Baku weren't native to the planet.

There was that one episode where they tried to save a planet from Satan. I dont think the planet was technically pre-warp, though, especially since there were federation scientists/engineers on the planet working with the population.

I think these two are almost if not entirely exclusionary. It cannot be Federation space if the inhabitants are pre-warp.

There are prime directive eff-ups. Like the flower bed trespasser assassins of S1 TNG. The Fed is in contact with the Edo although they shouldn't be but somehow s happened. We don't really know where they're located in reference to everything else in the Fed or the universe. But even if everything around them was warp hopping mad, the system of the Edo or at least their planet Rubicun III should be an exclave. In the scenario where the Fed would have to defend them from a hypothetical anti-prime-direxxer it could be a protectorate but not Fed territory.

I can think of two other instances with the PD that come close to this scenario but are no cigar. Data's long-fingered pen pal Salenka or something like that and Worf's adopted brother trying to save his knocked up pre-warp Penny Johnson. In both cases I don't think we know if the territory was Fed, Fed adjacent, or something else. And it's a moot point anyway because they were defending against natural disasters, not other species.

There's the TNG episode where Federation scientists are observing a non-warp capable civ from on the planet, when an accident exposed their lab and the aliens take one of the scientists hostage thinking they are demons. In this case, the external influence they are trying to limit and fix is the federation itself.

There is also another in the same vein where Data is damaged during an away mission on a planet with a non-warp capable civ and inadvertently is spreading radioactive material around the settlement because he lost his memories, and then has to correct all the damage when he is repaired.

These are the only two I can think of that even come close while also being within Federation space. As others have pointed out, the Voyager episode where they run into the Farenghi that ended up there from another episode of TNG is the exact thing you are asking... Just not in the right part of space.

The Prime Directive is that the Federation won’t interfere with the development of a pre-warp society.

It is NOT foreign policy that they try to enforce against other warp-capable civilizations.

A couple that come to mind is VOY “False Prophets” where they expel a couple parasitic Ferengi or ENT “Civilization” where warp-capable aliens are causing toxic pollution in a pre-warp society.