Doctor Who has a penchant for such …erm… homages. With a stable of Trek properties coming out, maybe they could consider a similar approach.
Dead Poet Society. Lecturing Q, Picard recites Shakespeare with passion. The entire bridge crew goes: o Captain, my Captain!
Set as a CAGE era film, Horatio Hornblower (1951) starring Gregory Peck. His discomfort around women is similar to Captain Pike's. USS Enterprise instead of the HMS Lydia. Klingons instead of Spanish. Rebel Klingon (House of Duras) working with the Romulans instead of "El Supremo" working with the French.
Which performance came first? I think Star Trek was first. Cause and Effect? Noticed Greg Peck on the jacket, too.
Back To The Future: Lt Junior Grade Picard's son uses a time machine to escape Klingon terrorists and ends up in the past where he causes by accident Cadet Picard to be stabbed through the heart by a Nausicaan. Picard's son disappears. The end!
Ismael by Barbara Hambly (1985) also featured mentions of characters from other science fiction and western movies & television shows - Including Bonanza. https://en.wikipedia.org/wiki/Ishmael_(Star_Trek) See my posts number 49 and 51 in the thread: https://www.trekbbs.com/threads/star-trek-is-part-of-mcu.293148/page-3#post-12916938
Avengers: Endgame Our heroes use time travel to save the planet after their enemy is able to achieve it's goal
A Clockwork Orange: After being brainwashed Worf can no longer fight against holodeck monsters, get hit by painsticks, eat live food, advise Picard to blow the hell out of a ship without feeling nauseous... Unfortunately, the same goes for listening to Klingon Operas!!!