Maybe master longing to fill unfinished part of school year (7)
I believe the answer is:
teacher
'maybe master' is the definition.
(I know that head teacher is a type of teacher)
'longing to fill unfinished part of school year' is the wordplay.
'longing' becomes 'ache' (longing can mean aching or pining for something).
'to fill' means one lot of letters goes inside another.
'unfinished' means to remove the last letter.
'part of school year' becomes 'term' (I've seen this before).
'term' with its final letter taken off is 'ter'.
'ache' going within 'ter' is 'TEACHER'.
(Other definitions for teacher that I've seen before include "Hectare (anag)" , "CARRY ON FILM" , "Schoolmaster/mistress" , "One who educates" , "One who might give lines" .)