I’d have thought that the music written was always more than they need, the way there’s extra music for Hoth or parts of Leia’s theme.
That’s not usually how it’s done. Recording music costs time and money so they don’t really want to be making things they aren’t going to use - just like deleted scenes aren’t shot with the purpose of being cut. It depends on the composer but with Williams on Star Wars, he’s scoring directly to the edited picture, in places he and the director have decided should have a score.
Where you might be getting confused is something like the Princess Leia theme suite - that’s a piece that was written and recorded parallel to the film’s score itself and was never intended to be used in the film (and, indeed, that recording has never been used in a SW) but was included on the soundtrack album. Composers often write concert suites for themes from their films and include them as pieces on albums, and/or perform them at concerts.