Examined? That's not new after half-term (7)
I believe the answer is:
perused
'examined?' is the definition.
(perusing is a kind of examining)
'not new after half-term' is the wordplay.
'not new' becomes 'used' (used or pre-owned as opposed to new).
'after' is a charade indicator (letters next to each other).
'half' means to take half the letters.
'term' becomes 'period' (a term is a period of time).
'period' with half the letters taken is 'per'.
'used' put after 'per' is 'PERUSED'.
'that's' is the link.
(Other definitions for perused that I've seen before include "Studied" , "Read (something) very carefully" , "Browsed" , "Scanned" .)