Speedy raid - people start inside! (5)
I believe the answer is:
rapid
'speedy' is the definition.
(I know that speedy can be written as rapid)
'raid people start inside' is the wordplay.
'start' says to take the initial letters.
'inside' indicates putting letters inside.
The initial letter of 'people' is 'p'.
'raid' enclosing 'p' is 'RAPID'.
(Other definitions for rapid that I've seen before include "Fast, speedy" , "Swift, speedy" , "Flying" , "Showing pace" , "Express" .)