Formal residence for the swine accommodating chief (7)
I believe the answer is:
starchy
'formal' is the definition.
('starchy' can be similar in meaning to 'formal')
'residence for the swine accommodating chief' is the wordplay.
'residence for the swine' becomes 'sty'.
'accommodating' is an insertion indicator.
'chief' becomes 'arch' ('arch' can be a synonym of 'chief').
'sty' enclosing 'arch' is 'STARCHY'.
(Other definitions for starchy that I've seen before include "Conventional" , "Stiff, formal" , "Stiff and formalistic" , "Unbending" , "Stiff, like potatoes" .)