Public service, something with no end, no beginning (7)
I believe the answer is:
utility
'public service' is the definition.
(I've seen this before)
'something with no end no beginning' is the wordplay.
'something with no end' becomes 'futility' (something with no point or end).
'no beginning' means to remove the first letter.
'futility' with its first letter removed is 'UTILITY'.
(Other definitions for utility that I've seen before include "gas, for example" , "Gas, electricity, etc" , "A useful thing like electricity company?" , "State of being useful" , "Service such as electricity or water" .)