Awfully scared when drinking one cocktail (7)
I believe the answer is:
sidecar
'cocktail' is the definition.
(I know that Sidecar is a type of cocktail)
'awfully scared when drinking one' is the wordplay.
'awfully' indicates an anagram.
'when drinking' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'scared' with letters rearranged gives 'sdecar'.
'sdecar' enclosing 'i' is 'SIDECAR'.
(Other definitions for sidecar that I've seen before include "Is raced (anag.)" , "passenger compartment" , "One-wheeled compartment attached to a motorcycle" , "Part of combination" , "Attachment to motorcycle to accommodate passenger" .)