You start with a hypothesis, to look for a logical explanation for unexplained things. As you collect evidence, you can then speculate on a theory. It remains a theory until it is proven.
You have used the word "proven" that is not something that you should use in this context since it is both a loaded word and subject to several meanings.
You mostly describe a process in that statement you don't do much in the way of defining a theory. The phrase "logical explanation" begins to suggest some idea of it. Perhaps you could have another go at the definition?
A gap in a theory to me, is an evidence or the lack thereof that would go against the theory. I guess I should use the word flaw in a theory, instead of a gap
Obviously evidence which goes against a theory is a suggestion that there is a flaw in the theory. The evidence isn't the flaw itself I'd say if I wanted to be dammed pedantic. Lack of evidence is much, much less likely to be useful in improving a theory as it most frequently simple means just that something has yet to turn up or is beyond the technology that is availble to test.
A true gap or flaw would be something that the theory should explain but can not; at least to me. An example of this in the original Darwinian forumlation was the lack of a mechanism for hereditity. In fact, a serious flaw should have been apparent with the idea about blended inheritance of the time. Blending as, I think, some saw it then would not allow the new features of an organism to not be washed out in a population.