Rank deal: more cut off (7)
I believe the answer is:
earldom
'rank' is the definition.
(I know that earldom is a type of rank)
'deal more cut off' is the wordplay.
'cut' means to remove the last letter.
'off' indicates anagramming the letters.
'deal'+'more'='dealmore'
'dealmore' with its last letter removed is 'dealmor'.
'dealmor' anagrammed gives 'EARLDOM'.
(Other definitions for earldom that I've seen before include "Norfolk or Wessex, for example" , "Essex?" , "A noble's lands or title" , "Title or estates of a nobleman" , "Domain of a mid-ranking peer" .)