have a lot of promise

To have a great amount of potential for future success or excellence. That fullback has a lot of promise—no wonder several professional football teams are looking to draft him as soon as he graduates. This new treatment we're developing has a lot of promise, but we won't know just how effective it is until it has been in use for a few years. The experiment had a lot of promise on paper, but it did not yield the results we were hoping for once we started working in the lab.