Rushed right in, dead beat (6)
I believe the answer is:
darted
'rushed' is the definition.
(darting is a kind of rushing)
'right in dead beat' is the wordplay.
'right' becomes 'rt'.
'in' is an insertion indicator.
'beat' indicates anagramming the letters.
'dead' with letters rearranged gives 'daed'.
'rt' put within 'daed' is 'DARTED'.
(Other definitions for darted that I've seen before include "Moved quickly and suddenly" , "Was fleet" , "Dashed, on the electric train?" , "Moved suddenly like game missile" , "Sniped" .)