Rush with indecent haste? (6)
I believe the answer is:
streak
'rush' is the definition.
(thesaurus)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for streak that I've seen before include "Unbroken series of events" , "Strip of a different colour" , "Naked public appearance" , "Long band" , "Run naked in a public place" .)