Busy teashops needing to save time straightaway (9)
I believe the answer is:
posthaste
'straightaway' is the definition.
(doing something posthaste is doing it immediately)
'busy teashops needing to save time' is the wordplay.
'busy' indicates anagramming the letters.
'needing to save' means one lot of letters goes inside another (inserted letters are held or saved).
'time' becomes 't' (abbreviation).
'teashops' with letters rearranged gives 'posthase'.
'posthase' placed around 't' is 'POSTHASTE'.
(Other definitions for posthaste that I've seen before include "Hurry the mail with utmost speed" , "As quickly as possible" , "Speedily" , "immediately" , "With utmost speed -- to the pass (anag)" .)