For Star Trek soundtrack albums from the 1980s, complete performer credits are often surprisingly difficult to find unless the label published detailed liner notes.

For Star Trek IV: The Voyage Home and its soundtrack album, these are the known credited musicians, bands, and contributors:

Main score
Leonard Rosenman — composer and conductor of the orchestral score
Alexander Courage — original Star Trek TV theme used/adapted in the score
Jazz fusion/source music

The film prominently uses music by Yellowjackets:

“Market Street”
“Ballad of the Whale”

The band members at that time were approximately:

Russell Ferrante — keyboards
Jimmy Haslip — bass
William Kennedy — drums
Marc Russo — saxophone

The soundtrack credits specifically mention “additional music” by Russell Ferrante, Jimmy Haslip & The Yellowjackets.

Punk band in the bus scene

The famous bus-scene punk song “I Hate You” was performed by the fictional punk group Edge of Etiquette. The music was created specifically for the film by:

Kirk Thatcher — writer/performer
Mark Mangini — arranger/sound work

The recording reportedly involved Thatcher and members of the sound department recording it quickly and cheaply to sound authentic.

Other credited music contributors
Craig Huxley — “Genesis Project” music cue
Ralph Ferraro — orchestrations for the score