Beginning with one’s off-time (5)
I believe the answer is:
onset
'beginning' is the definition.
(onset is a kind of beginning)
'with one's off-time' is the wordplay.
'with' says to put letters next to each other.
'off' indicates an anagram.
'time' becomes 't'.
'ones' anagrammed gives 'onse'.
'onse' next to 't' is 'ONSET'.
(Other definitions for onset that I've seen before include "Assault; start" , "Start, beginning" , "Beginning or early stages" , "Outbreak" , "Start - opening moments" .)