Here is Terminator: Hunter Killer. Even though a short film, it is better than the official (except T2) sequels. And most other ancillary stuff from the franchise, frankly. Says the creator:
TERMINATOR: HUNTER KILLER is a proof-of-concept short film, set in the future war of the Terminator-movie universe, as the humans struggle to survive in the post-apocalyptic wasteland following ‘Judgment Day’.
Proof of concept, eh? Well, it’s a long shot that the studio would let this guy do something. At best, they usually send a cease and desist and if the artist is lucky, hire him.
This is what fans have wanted for 30 years. You could say an attempt was made with Terminator: Salvation, but even the R-rated version of that does not cut the mustard.