Writers GUILD of America, not Union.
I'm certain the Roddenberry estate/heirs gets something for anything spun off of
Star Trek, because that's what the WGA MBA (Minimum Basic Agreement) specifies. Gene could sell his rights to the show(s) and he'd have no control and no say, but he'd still get a cut of the writing fees because of said WGA MBA.
@BillJ [edit] Staff writers are handled somewhat differently than freelancers because they are on the payroll, so I don't think John DF Black got paid again when Kevin Riley reappeared, since he created Riley while on staff. The same would apply to characters like Sarek, Kor, etc.
Not sure how excerpts from previous episodes are handled. The writers probably don't get paid for those given how brief they are.
The rules here are a little slippery because there are so many possible edge cases, which is why such matters sometimes end up in WGA Arbitration.