Endure English fellow turning over something inherited from father (4,4)
I believe the answer is:
last name
'something inherited from father' is the definition.
'endure english fellow turning over' is the wordplay.
'endure' becomes 'last' (synonyms).
'english' becomes 'e' (abbreviation).
'fellow' becomes 'man' (fellow can mean a man).
'turning over' says the letters should be written in reverse.
'e'+'man'='eman'
'eman' backwards is 'name'.
'last'+'name'='LAST NAME'
(Other definitions for last name that I've seen before include "Family identifier" , "Smith, say" , "Final appellation held by all members of a family" , "Part of appellation denoting family" .)