With this beast, some women make rapid progress (6)
I believe the answer is:
wombat
'with this beast some women make rapid progress' is the definition.
'wombat' can be an answer for 'beast' (wombat is a kind of beast). I'm unsure of the rest of the definition.
'with this beast some women' is the wordplay.
'with' means one lot of letters go next to another.
'this beast' becomes 'womb' (I can't justify this - if you can you should give a lot more credence to this answer).
'some' says to take the centre.
'women' becomes 'cats' (cat is a kind of woman).
The middle of 'cats' is 'at'.
'womb' next to 'at' is 'WOMBAT'.
Can you help me to learn more?
(Other definitions for wombat that I've seen before include "Burrowing animal" , "Australian resident" , "Bear-like marsupial" , "Marsupial of Oz" , "Australian animal resembling small bear" .)