I rushed round after second cocktail (7)
I believe the answer is:
sidecar
'cocktail' is the definition.
(I know that Sidecar is a type of cocktail)
'i rushed round after second' is the wordplay.
'rushed' becomes 'raced' ('race' can be a synonym of 'rush').
'round' says the letters should be written in reverse.
'after' means one lot of letters go next to another.
'second' becomes 's' (common abbreviation).
'raced' reversed gives 'decar'.
'i'+'decar'='idecar'
'idecar' put after 's' is 'SIDECAR'.
(Other definitions for sidecar that I've seen before include "Is raced (anag.)" , "Appendage to motor cycle" , "Motorbike passenger attachment" , "Cocktail of brandy, orange liqueur and lemon juice" , "Attachment on motorcycle to carry passenger" .)