His work for The Incredibles and Mission: Impossible III were fantastic.
The Incredibles had a nice, thirties/40s style of hero music that was not a parody, it was a genuine score as if it were any normal super hero movie. He intertwined nods to John Williams, John Barry, Jerry Goldsmith et al without making sound as if it were a parody.
I reckon it will be very similar to the way Goldsmith handled TMP. Giachinos score will go on in scenes, and somewhere along the line, TOS theme will be worked in. Much like uantum of Solace, where the bond theme was ver subtly spliced into little scenes, as if a nod to what Bond will become. Same as Casino Royale, the theme wasnt heard until the end.
When Star Trek becomes Star Trek in this movie, maybe we'll here it.
Who knows.
There are themes in The Incredibles that would make a very good Trek score.