Entering wager, way the woman makes big paper (10)
I believe the answer is:
broadsheet
'big paper' is the definition.
'broadsheet' can be an answer for 'paper' (I've seen this before). I'm unsure of the 'big' bit.
'entering wager way the woman makes' is the wordplay.
'entering' indicates putting letters inside.
'wager' becomes 'bet' (synonyms).
'way' becomes 'road' (road is a kind of way).
'the woman makes' becomes 'she' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'road'+'she'='roadshe'
'bet' placed around 'roadshe' is 'BROADSHEET'.
Can you help me to learn more?
(Other definitions for broadsheet that I've seen before include "Large-format newspaper" , "Our sort of paper" , "cover for king-size mattress?" , "Paper that can cover large issue" , "Something big that gets blanket coverage" .)