Streaker's business to be pursued by police (5)
I believe the answer is:
comet
'streaker's' is the definition.
(something which 'streaks')
'business to be pursued by police' is the wordplay.
'business' becomes 'co'.
'to be pursued by' means one lot of letters go next to another.
'police' becomes 'met' (I've seen this in other clues**).
'co'+'met'='COMET'
(Other definitions for comet that I've seen before include "Halley's phenomenon in space" , "Celestial body - early jet aircraft" , "Early jetliner" , "Object in space with bright centre and long hazy tail" , "Traveller round sun" .)