Family member hurries to get rid of it (7)
I believe the answer is:
stepson
'family member' is the definition.
(I've seen this before)
'hurries to get rid of it' is the wordplay.
'hurries' becomes 'stepsonit'.
'to get rid of' suggests deleting specific letters.
'stepsonit' with 'it' taken out is 'STEPSON'.
(Other definitions for stepson that I've seen before include "Relation, not by blood" , "No pests (anag)" , "Spouse's child from previous marriage" , "partner's sprog" , "younger member of family" .)