Hollywood star discarding old clothes (4)
I believe the answer is:
garb
'clothes' is the definition.
(garb is a kind of clothes)
'hollywood star discarding old' is the wordplay.
'hollywood star' becomes 'Garbo' (actress Greta Garbo).
'discarding' is a deletion indicator.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'garbo' with 'o' taken out is 'GARB'.
(Other definitions for garb that I've seen before include "something to wear" , "Apparel, attire" , "Raiment" , "Attire, clothing" , "Dress - habit" .)