Bear ought to run after European (8)
I believe the answer is:
shoulder
'bear' is the definition.
(both can mean to carry or take responsibility for)
'ought to run after european' is the wordplay.
'ought to' becomes 'should' ('you ought to' means 'you should').
'run' becomes 'r' (cricket abbreviation).
'after' means one lot of letters go next to another.
'european' becomes 'E' (abbreviation e.g. EU).
'r' put after 'e' is 'er'.
'should'+'er'='SHOULDER'
(Other definitions for shoulder that I've seen before include "Part of the body (that bears burdens?)" , "Undertake (burden)" , "Top of the arm" , "Cut of meat" , "Joint between the neck and arm" .)