Run to the end of the street, fast! (5)
I believe the answer is:
fleet
'fast' is the definition.
('fleet' can be similar in meaning to 'fast')
'run to the end of the street' is the wordplay.
'run' becomes 'flee' (I've seen this before**).
'to the end of' suggests the final letters.
The final letter of 'street' is 't'.
'flee'+'t'='FLEET'
(Other definitions for fleet that I've seen before include "Ships - quick!" , "Naval force or collection of buses" , "Swift - London street" , "Fast moving" , "Collection of company cars" .)