Family member, thin, refusing starter (4)
I believe the answer is:
aunt
'family member' is the definition.
(I've seen this in another clue)
'thin refusing starter' is the wordplay.
'thin' becomes 'gaunt' (similar in meaning).
'refusing starter' means to remove the first letter.
'gaunt' with its first letter removed is 'AUNT'.
(Other definitions for aunt that I've seen before include "Parent's female sibling" , "Charley's ___ , farce staged in London in 1892, revived and adapted ever since" , "Tuna gone bad for the relative" , "Wife of one's uncle" , "Parent's sister" .)