Going by the Star Trek: Discovery experience, the risk isn't being overshadowed by TOS - the risk is treading too heavily on it. It was a bit of a relief when Discovery jumped to the future and stopped stomping all over the things covered by or discovered by TOS.
I really enjoyed Anson Mount and Rebecca Romijn as Pike and Number One during Discovery's second season. And I'm thrilled by some of their choices of characters. But there's one looming thorn. How will they handle La'an Noonien-Singh? She's not simply Chekhov's gun waiting to go off - she's Chekhov's howitzer. She could be handled with some subtlety (which brings up the question why even have her obvious connection to Khan) or she can be an irritation intruding on TOS stories. Given Discovery's track record, I'm battening down the hatches in expectation of the latter but desperately hoping for the former.