Be unhappy to put me out of work (4)
I believe the answer is:
mope
'be' is the definition.
(moping is a kind of being)
'me out of work' is the wordplay.
'out of' indicates putting letters inside.
'work' becomes 'op' (common abbreviation for 'opus').
'me' going around 'op' is 'MOPE'.
'unhappy to put' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for mope that I've seen before include "Sulk; mooch" , "Be listless and apathetic" , "listless person" , "Languish" , "Pine - sulk" .)