Going off over key lessees sounding difficult to please (4,11)
I believe the answer is:
high maintenance
'difficult to please' is the definition.
(high maintenance can mean hard to please)
'going off over key lessees sounding' is the wordplay.
'going off' becomes 'high' (high can mean decaying or going off).
'over key' becomes 'main' (I've seen this in another clue. I am not sure about the 'over' bit.).
'lessees' becomes 'tenants' (I've seen this in another clue).
'sounding' shows a homophone (sound like).
'tenants' sounds like 'tenance'.
'high'+'main'+'tenance'='HIGH MAINTENANCE'
(Another definition for high maintenance that I've seen is " Demanding substantial amount of money".)