Bear ought to be scratching head by river (8)
I believe the answer is:
shoulder
'bear' is the definition.
(both can mean to carry or take responsibility for)
'ought to be scratching head by river' is the wordplay.
'ought to' becomes 'should' ('you ought to' means 'you should').
'scratching head' means to remove the first letter (the first letter or head is scratched out).
'by' is a charade indicator (letters next to each other).
'river' becomes 'r' (abbreviation).
'be' with its first letter taken away is 'e'.
'should'+'e'+'r'='SHOULDER'
(Other definitions for shoulder that I've seen before include "Body part of a strange old usher" , "Old usher, oddly, is part of the body" , "See 10" , "hard on the motorway" , "Part of the body (that bears burdens?)" .)