Here’s the history of the TMP Enterprise model post-movies:
1. During post-production of the first season TNG episode “The Battle,” Picard’s old ship, the Stargazer, was supposed to be a reuse of the TMP Enterprise model. That would have been the first time the model would have been used on screen post-The Voyage Home. However, modelmaker Greg Jein built a new filming model based on the small yellow kitbash in the Ent-D’s ready room in time for filming, so the TMP model was never used.
2. The wrecked TMP Enterprise model built specifically for the ship’s destruction in STIII was used as random ship wreckage in “Best of Both Worlds’ Pt. 2,” first as a wrecked saucer in the first scene, and part of the engineering hull in a later scene. Contrary to what was stated above, the TMP model was NOT used in “Unification.”
3. The wrecked saucer was again used as a stand-in when the Galaxy class U.S.S. Odyssey was destroyed in “The Jem’Hadar.” It was supposed to represent the Odyssey’s saucer being destroyed, despite it not being the same class.
4. The same wrecked saucer section above was later used as wreckage of the U.S.S. Olympia in the DS9 episode “The Sound of Her Voice.” It had crashed on a planet.
5. The animated Short Trek “Ephraim & Dot” shows the TMP Enterprise, although it is just a cartoon version.
So the original TMP filming model was never once seen on screen in TNG, DS9, VOY, ENT, DSC, or PIC, not even as stock footage. Plastic model kits or Franklin Mint metal models of the ship were used as desktop models in TNG, but that’s about it. The main reason why the model was never used as a guest ship was because it was a very unwieldy model to film. Its proportions made it very hard for the camera to get good angles of it. That’s why other ships were designed to be flatter, such as the Excelsior and the Enterprise-D: they were much easier to film.