Which one? I Netflix'ed my way through that whole show a couple years ago and didn't see any like that.
It does sound a little bit like "Space Seed" from TOS though, except I don't remember that ship having a particular destination. There was another TOS episode where they find a stray asteroid that turns out to actually be a generation ship inside. And there was some TNG episode where they find a ship with some 20th-century Earthers in cryogenic storage because they had just died of medical ailments. But I don't remember any ENT episodes like this, just some talk about "slow" Earth ships traveling at only Warp 1.5 or so, so that people lived their whole lives on them while on long-term trading missions (their helmsman came from one of these ships).
I'm pretty sure you're wrong and it was an episode of 'The Next Generation, although I've no idea what the title of the episode was... [0]
[0] I've watched the episode only once (I'm not a Trekkie :) ), but if I remember correctly a synopsis of the plot was that decades (at least...) ago an automated ship containing Klingons in cryogenic suspension was launched to colonise a distant planet; in the time following the launch of that ship, the Federation reached and colonised that planet using faster ships, unaware that the Klingon ship was on the way...
The crew of the Enterprise [D] has to try to figure out how to stop the Klingon ship from introducing the Federation colonists on the planet to the magic of orbital bombardment (a casus belli) without destroying the Klingon ship (a casus belli).
I think you're mixing up some details of that episode. The closest episode I can think of that matches that is "The Ensigns of Command", which involves a colony of humans that were isolated and underdeveloped due to interference from the planet's radiation. The colony was on a planet that technically belonged to the "Sheliak", a mysterious race the Federation had limited contact with, but who had decided to begin colonizing the planet and gave the Federation a short time span to remove the humans before they would eradicate them.
I looked it up, and the title of the episode was "The Emissary" [S2E20] (although, yes, either I remembered a few details incorrectly or the Wikipedia synopsis of the plot is incomplete).
There's one episode where they visit a colony established decades previous by a warp 1 or warp 2 ship, but they don't beat the colonists to the planet.
It does sound a little bit like "Space Seed" from TOS though, except I don't remember that ship having a particular destination. There was another TOS episode where they find a stray asteroid that turns out to actually be a generation ship inside. And there was some TNG episode where they find a ship with some 20th-century Earthers in cryogenic storage because they had just died of medical ailments. But I don't remember any ENT episodes like this, just some talk about "slow" Earth ships traveling at only Warp 1.5 or so, so that people lived their whole lives on them while on long-term trading missions (their helmsman came from one of these ships).