Piggy is stylish around home (7)
I believe the answer is:
swinish
'piggy' is the definition.
(synonyms)
'stylish around home' is the wordplay.
'stylish' becomes 'swish' (similar in meaning).
'around' means one lot of letters goes inside another.
'home' becomes 'in' ('he's home' can mean 'he's in').
'swish' enclosing 'in' is 'SWINISH'.
'is' is the link.
(Other definitions for swinish that I've seen before include "Like a cad" , "Piglike" , "like Eumaeus's charges" , "Piggy" , "Porcine" .)