State in which there's no point heading off for public service (7)
I believe the answer is:
utility
'for public service' is the definition.
(I've seen this before)
'state in which there's no point heading off' is the wordplay.
'state in which there's no point' becomes 'futility' (futile or pointless state).
'heading off' means to remove the first letter.
'futility' with its first letter taken away is 'UTILITY'.
(Other definitions for utility that I've seen before include "water provider, say" , "Service such as electricity or water" , "Gas, electricity, etc" , "gas, for example" , "Usefulness" .)