Relentless outside losing vote (7)
I believe the answer is:
eternal
'relentless' is the definition.
(thesaurus)
'outside losing vote' is the wordplay.
'outside' becomes 'external' (synonyms).
'losing' suggests deleting specific letters.
'vote' becomes 'x' (how votes are marked).
'external' with 'x' taken away is 'ETERNAL'.
(Other definitions for eternal that I've seen before include "Forever and always" , "always to be remembered" , "abiding" , "Forever or unchanging" , "Without beginning or end" .)