Anshuman, what you are suggesting sounds like moving both your lover and your mistress in under the same roof. They may not be compatible! However you asked for help, so I´ll try. A word of caution :- I am not familiar with the star trek series ( games that is ) so it´s possible that I´ll put my foot in it from time to time. Bear with me.
Firstly you need a goal. Why put the two of them together? What will you achieve by doing so?
Then you need plausability. It has to make sense, otherwise it will fly like a lead balloon.
Do both games occupy the same space?( physically that is ). If yes, then you need to take the time factor into account.
If the games occupy adjacent space, you do not. The difference can be explained as being due to the use of different calendar systems. Check out our own history, we have had lots of different calendar systems, many of them concurrently.
The difference in technology achievement could be explained as follows :- both groups have common ancestry, their forefathers are pioneers ( viz Pilgrim fathers perhaps ) who reach a stage where they have to decide between two one-way jump points. Lacking unity, one group “goes left” the other “goes right”. In time, the local conditions – raw materials, climate, pressure from alien races – would determine the rate of development of each group.
How are you physically going to do it? So far this seems to be the main point of interest in the thread replies. There have been good suggestions to solve that :- “Q factor” “Worm hole” so I´ll put in the “Star Gate” option.
As I see it, the really big question is “What are they going to do when they meet?”
Will they just say “Hi, nice to meet you” and then disappear back to where they came from? Form an alliance against a common enemy? Consider the other a threat to their own survival and start an intergalactic war? The WC “faction” could balance the tech difference by discovering/rediscovering steltek sites ex. P1.???
The possibilities are endless, the effort needed to succeed enormous, but then the prize would also be great.
Good luck!