An emerging artist is someone who's in the early stage of their career, someone who's caught the eye of an art critic and/or gallery, but hasn't yet established a solid reputation as an artist amongst art critics, art buyers, and art galleries.
The term emerging artist is often used for young and recently graduated from a prestigious art college, but can also apply to someone who's made a career change or recently decided to prioritize their art above everything else.
You could say it's a label art galleries use because it sounds better than "new artist" or "unknown artist".
