a lot of promise
A great amount of potential for future success or excellence. The fullback showed a lot of promise in college, with several professional football teams looking to draft him as soon as he graduated. 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.
*lot of promise
much promise for the future. (*Typically: have ~; show ~.) Sally is quite young, but she has a lot of promise. This bush is small, but it shows a lot of promise.