Once right to cry out (7)
I believe the answer is:
'cry out' is the definition.
'once right' is the wordplay.
'once' becomes 'ex' (prefix meaning former or onetime).
'right' becomes 'claim' (claim is a kind of right).
'to' is the link.
(Other definitions for exclaim that I've seen before include "Shout out" , "Announce vehemently" , "Cry out (in shock, etc)" , "Speak suddenly" , "Express surprise" .)