Family member welcomes a vote for rest (10)
I believe the answer is:
relaxation
'rest' is the definition.
('relaxation' can be a synonym of 'rest')
'family member welcomes a vote' is the wordplay.
'family member' becomes 'relation' (I've seen this before**).
'welcomes' is an insertion indicator (in sense of 'invites in').
'vote' becomes 'x' (how votes are marked).
'a'+'x'='ax'
'relation' enclosing 'ax' is 'RELAXATION'.
'for' acts as a link.
(Other definitions for relaxation that I've seen before include "repose" , "Chilling out" , "leisure" , "(Period of) rest" , "fun" .)