Clue: Old boy given 'eave up — one going from bar to bar? (6)
Answer: OBOIST
Explanation: Definition: one going from bar to bar
 OB(abbrev. for "old boy" of, say, a school or university) **plus**(given) 'OIST("hoist"/to haul up** minus its 1st letter, similar to** "heave"/to haul up **minus its 1st letter**).
Defn: One playing/going from bar to bar, a bar being one of the sections into which a piece of music is divided.