Cat put in bag — hard to bear (7)
I believe the answer is:
stomach
'bear' is the definition.
(synonyms)
'cat put in bag hard' is the wordplay.
'cat' becomes 'tom' (a tom is a male cat).
'put in' indicates putting letters inside.
'bag' becomes 'sac' (a small bag).
'hard' becomes 'h' (abbreviation used in pencil classifications).
'tom' placed into 'sac' is 'stomac'.
'stomac'+'h'='STOMACH'
'to' acts as a link.
(Other definitions for stomach that I've seen before include "Could Mac host this organ?" , "Digestive organ" , "stand" , "Appetite for food" , "Bear - belly" .)