I am looking for a couple of nouns that describe someone who is noticably improving at some learning activity. If someone is just starting they are a novice or a beginner; at the end, there are various words (expert, master, etc.). I am looking for words for someone who is a beginner, but who is markedly getting better, and for someone who is not an expert but is approaching it. I already thought of improver. It doesn't seem very satisfactory; neither does trainee, which doesn't imply improvement.
For the not beginner, not expert, you could use 'intermediate'.
You can get inspiration from this list
Somebody who picks up a skill very quickly is sometimes called a natural.
A person regarded as having an innate gift or talent for a particular task or activity.
For a person who knows the ropes, try adept.
A person who is skilled or proficient at something.
I've heard the term "student" used in this context. One might say, "XXX is a student of modern dance." or something similar.
The Dreyfus model of skill acquisition might be a useful scale.