Former favourite welcoming study about setter's stratagem (9)

I believe the answer is:
expedient
'stratagem' is the definition.
(thesaurus)
'former favourite welcoming study about setter's' is the wordplay.
I cannot really understand how this works, but
'former' could be 'ex' (prefix meaning former or onetime) and 'ex' is found within the answer.
'setter' could be 'i' (the person who set this crossword) and 'i' is found within the answer.
'study' could be 'den' (term for a study or office) and 'den' is found in the remaining letters.
'favourite' could be 'pet' (synonyms) and 'pet' is found in the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for expedient that I've seen before include "Appropriate though not necessarily fair" , "Means to get" , "Suitable for the circumstances rather than just" , "Serving to promote one's interest" , "Suitable or appropriate" .)
