Favouring Miss Doone, almost without hope (7)
I believe the answer is:
forlorn
'without hope' is the definition.
(thesaurus)
'favouring miss doone almost' is the wordplay.
'favouring' becomes 'for' (to be 'for' something is to be in favour of it).
'miss doone' becomes 'lorna' (I've seen this in another clue).
'almost' means to remove the last letter (most of the word but not all of it).
'lorna' with its last letter removed is 'lorn'.
'for'+'lorn'='FORLORN'
(Other definitions for forlorn that I've seen before include "Cheerless, desolate" , "Left alone and unhappy" , "Bereft" , "Miserable" , "Wretched" .)