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' indicates putting letters inside.
'respectable' becomes 'nice' (similar in meaning).
'e' inserted within '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?" .)