Rank older man, almost entirely drunk (7)
I believe the answer is:
'rank' is the definition.
(I know that earldom is a type of rank)
'older man almost entirely drunk' is the wordplay.
'almost entirely' means to remove the last letter (most but not all of the word).
'drunk' indicates anagramming the letters.
'olderman' with its final letter removed is 'olderma'.
'olderma' with letters rearranged gives 'EARLDOM'.
(Other definitions for earldom that I've seen before include "noble area of country" , "Peer's rank" , "A noble's lands or title" , "Domain of a mid-ranking peer" , "Essex?" .)