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 (some letters on the outside of others).
'work' becomes 'op' (abbreviation for opus).
'me' going around 'op' is 'MOPE'.
'unhappy to put' is the link.
I am not very happy about this link. Some or all of it may be part of 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" .)