Cat in bag: initially hard to put up with (7)
I believe the answer is:
stomach
'put up with' is the definition.
(synonyms)
'cat in bag initially hard' is the wordplay.
'cat' becomes 'tom' (a tom is a male cat).
'in' indicates putting letters inside.
'bag' becomes 'sac' (a small bag).
'initially' indicates taking the first letters.
The initial letter of 'hard' is 'h'.
'tom' going inside 'sac' is 'stomac'.
'stomac'+'h'='STOMACH'
'to' is the link.
(Other definitions for stomach that I've seen before include "Bag-like part of the alimentary canal" , "Endure; organ" , "Tolerate; appetite" , "Breadbasket (informal)" , "Saclike organ" .)