Hollywood star disposing of old clothes (4)
I believe the answer is:
garb
'clothes' is the definition.
(garb is a kind of clothes)
'hollywood star disposing of old' is the wordplay.
'hollywood star' becomes 'Garbo' (actress Greta Garbo).
'disposing of' suggests deleting specific letters.
'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 "Dress - habit" , "costume" , "Clothe" , "Fashion of dress" , "Dress - clothing" .)