Go round street with cocktail (5)
I believe the answer is:
skirt
'go round' is the definition.
(thesaurus)
'street with cocktail' is the wordplay.
'street' becomes 'st'.
'with' is an insertion indicator.
'cocktail' becomes 'kir' (I've seen this before).
'st' going around 'kir' is 'SKIRT'.
(Other definitions for skirt that I've seen before include "Garment below the waist" , "Item of female apparel" , "Try to avoid (a problem)" , "Go round the edges of" , "Feminine item of clothing" .)