Agreed to adopt pet that's "difficult" (11)
I believe the answer is:
complicated
'difficult' is the definition.
(thesaurus)
'agreed to adopt pet' is the wordplay.
'agreed' becomes 'complied' (complying is a kind of agreeing).
'to adopt' means one lot of letters goes inside another (inserted letters are taken in or adopted).
'pet' becomes 'cat' (cats are often kept as pets).
'complied' placed around 'cat' is 'COMPLICATED'.
'that's' acts as a link.
(Other definitions for complicated that I've seen before include "consisting of many interconnecting parts" , "Intricate, difficult" , "Tricky" , "confused" , "Not simple" .)