Terribly nice English family member (5)
I believe the answer is:
niece
'family member' is the definition.
(I've seen this in another clue)
'terribly nice english' is the wordplay.
'terribly' indicates an anagram.
'english' becomes 'e' (abbreviation).
'nice' with letters rearranged gives 'niec'.
'niec'+'e'='NIECE'
(Other definitions for niece that I've seen before include "girl further down the line" , "Young female relative" , "Family girl" , "Criminal" , "Brother's daughter" .)