The crossword solution for the term 'PROMISE's Partner, in phrase' is the word 'LICK'. This is a reference to the phrase 'a PROMISE is a PROMISE', which is used to emphasize the importance of keeping one's word. The phrase implies that if someone makes a PROMISE, they should be held to it and not take it lightly. The word 'LICK' is used to emphasize the seriousness of the PROMISE, as it implies that the person making the PROMISE should be willing to put in the effort to fulfill it.