Upgradeable contracts and Interfaces

Greetings,

If an upgradeable smart contract has an interface that other contracts use to interact with the current implementation, what happens to the interface when the current implementation changes? For example, if additional functions are added to the contract, should there be a new interface contract? Can interface contracts be upgraded as well?

If you are referring to proxy contract, that remains same. Only the implementation contract keeps changing. Proxy contract refers to implementation contract.