Pointlessness when cancelling key public service (7)
I believe the answer is:
utility
'public service' is the definition.
(utility can mean a public service)
'pointlessness when cancelling key' is the wordplay.
'pointlessness' becomes 'futility' (I've seen this before).
'when cancelling' suggests deleting specific letters.
'key' becomes 'f' (musical key).
'futility' with 'f' removed is 'UTILITY'.
(Other definitions for utility that I've seen before include "Supplier of gas or electricity" , "Service such as electricity or water" , "water provider, say" , "gas, for example" , "Usefulness" .)