Meaning of “promise” - Learner’s Dictionary

promise

noun uk us /ˈprɒmɪs/

B1 [ C ] a statement that you will certainly do something:

I'm not sure I can do it so I won't make any promises.
keep/break a promise

B2 to do/not do what you said that you would do

show promise

If someone or something shows promise, they are likely to be successful:

As a child, he showed great promise as an athlete.

(Definition of “promise noun” from the Cambridge Learner’s Dictionary © Cambridge University Press)