Job that's hard in the central part (5)
I believe the answer is:
chore
'job' is the definition.
(I know that job can be written as chore)
'hard in the central part' is the wordplay.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'in the' is an insertion indicator.
'central part' becomes 'core' (I've seen this before).
'h' going inside 'core' is 'CHORE'.
'that's' is the link.
(Other definitions for chore that I've seen before include "Tedious routine task" , "Onerous task" , "unwelcome task" , "burden" , "Task, job" .)