Though I’ve agreed elsewhere that Section 31 needs to be taken down, being Starfleet’s war crimes department, here I’m going to take a different tack:
Both Section 31 and the Klingon equivalent — what I’ll here arbitrarily call the Klingon Time Masters — have access to technology that can access both time travel and galactic-distance instant travel. Yet through all the back-and-forth between the Federation and the Klingons over the centuries, neither wiped out the other…
That’s because both organizations, while horribly ruthless, are also quite smart — and are willing to go beyond their originating cultures’ own values for what they see as the greater good, which both see more as long-term survival rather than overt conquest. They both involve themselves in quietly manipulating their civilizations toward this — which ultimately brings them together, as their views are actually closer to each other’s, rather than those professed by either Federation or Empire. By the time of the Temporal Wars — and possibly much earlier — what had been Section 31 and the Klingon Time Masters have in fact merged into a single faction on the galactic playboard.