A bet that rises in height (4)
I believe the answer is:
ante
'a bet that rises in height' is the definition.
'ante' can be an answer for 'a bet' (ante is a kind of bet). I am not sure about the remainder of the definition.
'a bet that rises' is the wordplay.
'a' becomes 'an'.
'bet' becomes 'et' (I can't justify this - if you can you should believe this answer much more).
'that rises' is a reversal indicator.
'et' in reverse letter order is 'te'.
'an'+'te'='ANTE'
Can you help me to learn more?
(Other definitions for ante that I've seen before include "not post" , "Each player's initial contribution to the pot" , "Preposition meaning before" , "early payment" , "Prefix meaning before" .)