It wasn't established on screen. Nor was much established about the Hur'q - DS9 "The Sword of Kahless" describes them as hit-and-run raiders rather than an oppressive occupying force, and ENT "Affliction" just name-drops them as invaders.
It's indeed the novels that take the Hur'q concept and evolve it towards what Barbara Hambly originally did with a species she called Karsids. The Hertzler&Lang The Left Hand of Destiny expands on the occupation and oppression concept, and Keith DeCandido's The Art of the Impossible describes how the Klingons got their FTL from the rebellion against the Hur'q.
You could also check out Hambly's Ishmael to see how the Hur'q compare to the Karsids; IMHO, they could well be the same folks, seen through two different lenses.
Outside this, there's DS9 "Little Green Men" where Quark gets stuck in the year 1947 and dreams of selling the secret of warp drive to the Ferengi, giving them a head start of "centuries" on humans, Klingons and Vulcans. But "centuries" is already very much stretching it as regards humans, and we know Vulcans were interstellar long before 1947 even if warp drive isn't explicated as their means. So we might be best off ignoring Quark, or rather thinking that now that he has the secret of time travel down pat, he will conduct the sale even farther back in history. After all, if he didn't have faith in further travel, he'd be stuck on Earth anyway. Thus, no real information on Klingon warp drive there...
Timo Saloniemi