Summary
Tate was one of the lone bright spots in an otherwise forgettable season for the Rockets. He rebounds well on the offensive end, is a solid multi-positional defender, and overall just makes winning plays on both ends. Tate could improve his outside shot, but he finishes well enough at the rim to make him an efficient offensive player.

Already 25 years old, Tate isn't a high-upside prospect, but there's little doubt in my mind that he can be a solid role player. Tate won't be waived this summer, so he won't become a free agent. 
 
Cap Considerations
Tate's $1.5 million salary for 2021-2022 is non-guaranteed, and if he is waived he will become an unrestricted free agent and the Rockets will have no form of Bird rights on him. It's very unlikely the Rockets waive Tate, and if he did he would likely be claimed before hitting free agency. If he is waived, teams could claim him off waivers, but would need to fit his salary within cap space or an exception to do so, as his contract doesn't fit within the minimum salary exception as it was a three-year contract.

If Tate becomes a free agent, other teams will have multiple ways to sign him as even teams without cap space could possibly use either of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE to sign him. I would also say that in the unlikely scenario Tate is waived and clears waivers, his value will have dropped low enough that he would only have offers for the minimum.