Bet it's time to wear coat for winter (5)
I believe the answer is:
wager
'bet' is the definition.
(I know that bet is a kind of bet)
'time to wear coat for winter' is the wordplay.
'time' becomes 'age' (an age is a period of time).
'to wear' is an insertion indicator (to wear something is to be covered up by it).
'coat for' means to remove the middle letters (the letters which coat the word).
'winter' with its middle taken out is 'wr'.
'age' placed into 'wr' is 'WAGER'.
'it's' is the link.
(Other definitions for wager that I've seen before include "better to put this on?" , "Risk; stake" , "(Place a) stake" , "Punt" , "stake required" .)