I'm reduced if not losing heart, and rash (11)
I believe the answer is:
improvident
'rash' is the definition.
('improvident' can be a synonym of 'rash')
'i'm reduced if not losing heart' is the wordplay.
'reduced' means to remove the last letter.
'if' becomes 'provided' (I've seen this before).
'losing heart' means to remove the middle letters.
'not' with its centre removed is 'nt'.
'provided' with its final letter taken away is 'provide'.
'im'+'provide'+'nt'='IMPROVIDENT'
'and' is the link.
(Other definitions for improvident that I've seen before include "Not thrifty" , "Careless" , "unprepared for what's to come?" , "Thoughtless" , "without forethought" .)