Chary at first, be inclined to criticise a fresh start (5,5)
I believe the answer is:
clean slate
'a fresh start' is the definition.
('clean slate' can be a synonym of 'fresh start')
'chary at first be inclined to criticise' is the wordplay.
'at first' indicates taking the first letters.
'be inclined' becomes 'lean' ('lean' can be a synonym of 'be inclined'**).
'to criticise' becomes 'slate' (I've seen this before).
The first letter of 'chary' is 'c'.
'c'+'lean'+'slate'='CLEAN SLATE'
(Other definitions for clean slate that I've seen before include "good record" , "A record without dishonour" , "new start" , "making a fresh start?" .)