Is foolish to finish with Times publication (5)
I believe the answer is:
dotes
'is foolish' is the definition.
(to dote is to behave foolishly)
'finish with times publication' is the wordplay.
'finish' becomes 'do'.
'with' means one lot of letters go next to another.
'times publication' becomes 'tes' (Times Educational Supplement).
'do'+'tes'='DOTES'
'to' acts as a link.
(Other definitions for dotes that I've seen before include "Shows great fondness, perhaps for spouse" , "Showers affection on" , "-- on, adores" , "Showers with love" , "Shows excessive love" .)