My guess it would be Giacchino (which I am fine with) because J.J. Abrams, who resuscitated the franchise, trumps Justin Lin who comes in as a hired director. Lin isn't even listed as an executive producer, which is usually thrown in as an enticement.
If that's the case, why isn't Giacchino scoring Mission: Impossible 5?
Perhaps because MISSION IMPOSSIBLE 5 like MISSION IMPOSSIBLE 1 is anchored with the Schifrin theme that any composer can adapt? While STAR TREK, even though it includes the Courage theme is anchored by Giacchino's music.
