A neuro-specialist was somebody whose particular field of study was neurology.
In 2368, Captain Jean-Luc Picard described Doctor Toby Russell in his log as a neuro-specialist. (TNG: "Ethics")
In the script, the term neuro-specialist is not used, but Crusher is said to have sent for a neurogeneticist instead. The field of neurogenetics is mentioned in the final episode.