Miss the ride the rest went off on (8)
I believe the answer is:
spinster
'miss' is the definition.
(I've seen this before)
'ride the rest went off on' is the wordplay.
'ride' becomes 'spin' (I've seen this in another clue).
'went off' is an anagram indicator.
'on' says to put letters next to each other.
'rest' with letters rearranged gives 'ster'.
'spin'+'ster'='SPINSTER'
'the' acts as a link.
(Other definitions for spinster that I've seen before include "Unmarried older woman" , "One spurning union activity" , "She never married" , "old maid, perhaps" , "woman like Miss Havisham" .)