UST was not able to be staked in a Proof-of-Stake system. UST was lent (to borrowers) via lending protocols, and in return the lenders earned interest. This interest was subsidized by Luna to encourage usage of the UST stablecoin.

USDT also doesn't incentivize holders of the token. Centralized or decentralized platforms may offer incentives for depositing token though, but this isn't done by Tether itself.