I went off right after cold period (6)
I believe the answer is:
winter
'cold period' is the definition.
(I've seen this before)
'i went off right' is the wordplay.
'off' indicates an anagram.
'right' becomes 'r' (common abbreviation**).
'i'+'went'='iwent'
'iwent' anagrammed gives 'winte'.
'winte'+'r'='WINTER'
'after' acts as a link.
(Other definitions for winter that I've seen before include "Time for mittens and scarves?" , "Cold period" , "'Now is the . . . . . . of our discontent' (Richard III)" , "'If . . . . . . comes, can spring be far behind?'" , "period of freeze?" .)