= leaves available the possibility of...

Charlie's and Diego's answers are good. I just want to mention that usually the wording is "hold open the promise" not "hold a promise open". And a similar expression is "hold open an offer" which is used when someone is offering something and the person does not need to accept immediately. ("My friend held open an offer to let me stay at his house if I was ever in his city.") To "hold open the promise" implies some kind of hope or possibility. ("Sustainable energy sources hold open the promise of a better future.")

The promise will be there for your, whenever you need it! :D E.g: You don't need to accept the deal now, but think about it and call me later. I will hold the promise open. :)