At the very least you need to describe exactly what the problem you're having is...and exactly where in the mission it's happening. Any additional info, screenshots and videos would also be helpful, so it can be found more easily and tested.
I don't know what the OP issue may be, but in the past I've had issues with not getting credit for killing the Tormenter of the Dead and with the game bugging out during the Storming the Gates portion. Both were corrected by repeated retries.
Yes often for the Klingon side of things you need to redo the mission, there are bugs a plenty in the Klingon starts for the Klingon Event and for Delta. Dropping the mission and restarting often fixes it, but not always, sometimes it takes two or more goes and sometime not even that works.
I created a klingon delta recruit and just finished running the entire klingon missions and it all worked fine. The Delta beacons are easy to miss though as they are not as lit up as they are for other missions, and you can easily go past them. The ones on Rura Penthe and the Forca III for the bat'leth tournament while trying to save M'Ven are very easy to miss if you are not careful, but they are there. Make good use of your scanner for those ones.
The Afterlife mission is often the one that will cause issues with not triggering the next stage, but for me on this run it ran through without a hitch, though there were some periods where there was a delay of up to 30 seconds before the next scene took place, which almost made me think it was glitching out.
I ran into the issue with Afterlife a couple of days ago, the Tormenter of the Dead didn't turn hostile after his initial dialogue. Had to abort mission and try again, second time worked like it should.
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The Afterlife mission is often the one that will cause issues with not triggering the next stage, but for me on this run it ran through without a hitch, though there were some periods where there was a delay of up to 30 seconds before the next scene took place, which almost made me think it was glitching out.