Time went off and ran (7)
I believe the answer is:
'ran' is the definition.
(trotting is a kind of running)
'time went off' is the wordplay.
'time' becomes 't' (abbreviation).
'went off' becomes 'rotted'.
'and' is the link.
(Other definitions for trotted that I've seen before include "Scampered" , "moved at a fair pace" , "Moved at fairly fast gait" .)