A scholar was a lifelong student of a particular field.
Vulcan had a number of great scholars. In 2287, Spock mentioned a particular "young student"'s banishment from Vulcan, saying that prior to his rejection of logic, the man was expected to take his place among them. (Star Trek V: The Final Frontier)
In 2364, upon admiring Data's painting of zylo eggs and hearing that Geordi La Forge had suggested the subject to him, William T. Riker felt that they should document the incident, as scholars might find it interesting that a blind man was teaching an android how to paint. (TNG: "11001001")
In 2369, the archaeologist Professor Richard Galen, angered by his former student Jean-Luc Picard's decision not to join him on an archaeological adventure, insulted him as amateurish, telling him "...as a scholar, you're nothing but a dilettante." On his deathbed, however, he admitted that he had been too harsh. (TNG: "The Chase")