"许诺获支持" can be translated into English as "a promise gains support" or "the promise receives support", depending on the specific context.
If you want to emphasize that a particular promise made by someone has started to receive backing or endorsement, "a promise gains support" would be appropriate.
If you're referring to a specific promise that has already been acknowledged or approved by others, "the promise receives support" could be used.
Both expressions convey the idea that a promise is being positively acknowledged or endorsed by others.