I hurried around in pursuit of small cocktail (7)
I believe the answer is:
sidecar
'cocktail' is the definition.
(sidecar is a kind of cocktail)
'i hurried around in pursuit of small' is the wordplay.
'hurried' becomes 'raced' ('race' can be a synonym of 'hurry').
'around' shows that the letters should be reversed in order.
'in pursuit of' means one lot of letters go next to another.
'small' becomes 's' (abbreviation - e.g. clothes size).
'raced' in reverse letter order is 'decar'.
'i'+'decar'='idecar'
'idecar' put after 's' is 'SIDECAR'.
(Other definitions for sidecar that I've seen before include "Motorbike passenger attachment" , "that's suitable for a non-driver" , "Cocktail - cedar is (anag)" , "Is raced (anag.)" , "One-wheeled compartment attached to a motorcycle" .)