Originally Posted by Dark Raven
I imagine it would be much like how it was dealt with in First Contact and Deep Space Nine where they talked about the Dominion War going on at the time. They referenced it in First Contact. Deep Space Nine adopted the First Contact uniforms. However, neither made a big deal about either of those things. They were both in continuity but separate enough as well to be their own autonomous thing.
The worst case scenario would be similar to comic series with good, well planned, story arcs that are constantly interruped with tie-ins to big events