Cook, large inside, getting more slender (7)
I believe the answer is:
slimmer
'more slender' is the definition.
('slim' can be a synonym of 'slender')
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for slimmer that I've seen before include "More slenderly built" , "One losing weight" , "person who's trying to lose weight" , "More slender" , "I aim to get rid of some" .)