Careless sister, heading off, runs into street (6)
I believe the answer is:
unwary
'careless' is the definition.
(thesaurus)
'sister heading off runs into street' is the wordplay.
'sister' becomes 'nun' (I've seen this before).
'heading off' means to remove the first letter.
'runs' becomes 'r' (cricket abbreviation).
'into' means one lot of letters goes inside another.
'street' becomes 'way' (I've seen this before).
'nun' with its initial letter taken off is 'un'.
'r' going into 'way' is 'wary'.
'un'+'wary'='UNWARY'
(Other definitions for unwary that I've seen before include "Off guard" , "Careless" , "Not alert or suspicious" , "Incautious and unprepared for danger" , "Runway (anag)" .)