Earl received by respectable relative (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'earl received by respectable' is the wordplay.
'earl' becomes 'e'.
'received by' is an insertion indicator.
'respectable' becomes 'nice' (similar in meaning).
'e' inserted into 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "A younger female relative" , "Female relation" , "Brother's daughter" , "Young female relative" , "[PRIEST'S] daughter?" .)