Right remains heedless (4)
I believe the answer is:
rash
'heedless' is the definition.
(thesaurus)
'right remains' is the wordplay.
'right' becomes 'r' (common abbreviation).
'remains' becomes 'ash' (I've seen this before).
'r'+'ash'='RASH'
(Other definitions for rash that I've seen before include "Impulsive - skin condition" , "Hives" , "Lacking in caution" , "Hotheaded" , "Over-hasty, reckless" .)