Small bird's run quickly (5)
I believe the answer is:
scoot
'run quickly' is the definition.
(I know that to scoot is to apace run)
'small bird's' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'bird' becomes 'coot' (coot is a kind of bird).
's'+'coot'='SCOOT'
(Other definitions for scoot that I've seen before include "Leave quickly" , "Skedaddle" , "Move with a rapid darting motion" , "hightail it" , "Move rapidly" .)