Public service’s lack of purpose when missing leader (7)
I believe the answer is:
utility
'public service's' is the definition.
(utility can mean a public service)
'lack of purpose when missing leader' is the wordplay.
'lack of purpose' becomes 'futility' (something futile has no purpose or effect).
'when missing leader' means to remove the first letter.
'futility' with its initial letter taken away is 'UTILITY'.
(Other definitions for utility that I've seen before include "Eg, gas supplier" , "Practicality - public service" , "water provider, say" , "State of being useful" , "A useful thing like electricity company?" .)