I was under the impression that Klingons were barely even interested in Earth and that region, at least for Enterprise era. I felt like the only power that Earth came into conflict early on were Romulans. Suliban too, but they were pretty much a product of temporal cold war and I also thought that their mysterious benefactor was actually a Romulan anyway.
Tholians would've made a nice appearance or Gorn, unfortunately they were mostly restricted to mirror universe.
And from little I've seen of DS9, Shran made a pretty good Dominion bad guy.
I regretted not seeing him in mirror universe episodes, but after I recently read Age of the Empress, I understood why.