I can think of six Trek cast members who were recurring members of Mission: Impossible
teams. In the original show, Leonard Nimoy was a regular team member for two seasons; Lee Meriwether and Barbara Anderson were both recurring members appearing in 6 and 7 episodes respectively; and Walker Edmiston
, who did uncredited voiceover work in several Trek episodes, played a voice impersonator named Dave in two seventh-season episodes. And in the '88 revival, one of the regular team members was Phil Morris, who would later make several Trek appearances. And, of course, Simon Pegg has been on the team in the last two M:I movies.
Trek players who were one-time M:I team members or collaborators in the original series include Eddie Paskey (essentially playing himself, a Hollywood stand-in, although he was named "Steve" in the script), George Takei, Barry Atwater, John Crawford (as two separate one-time characters), Arthur Batanides, William Schallert, Vic Perrin, Jack Donner, Vince Howard, Barbara Luna, Frank da Vinci (Nimoy's Trek/M:I stand-in, who played much the same role in-story), Antoinette Bower, Peter Brocco, Walker Edmiston (as a separate, one-shot character in season 6), and Lawrence Montaigne. (Perrin actually gets an extra half-credit here, since he overdubbed the voice of an actor whose character assisted the team in a season 5 episode.) I don't recall who, if anyone, played guest team members in the '88 revival.
Of course those are just Trek players who were actually on the IMF team or cooperating with it. Listing all the Trek guests in M:I would take all day.