Row involving stray dog (7)
I believe the answer is:
terrier
'dog' is the definition.
(terrier is a kind of dog)
'row involving stray' is the wordplay.
'row' becomes 'tier' (tier is a kind of row).
'involving' is an insertion indicator.
'stray' becomes 'err' ('err' can be a synonym of 'stray').
'tier' placed around 'err' is 'TERRIER'.
(Other definitions for terrier that I've seen before include "Part-time soldier" , "Bedlington - -" , "he's not a boxer" , "Dog - reservist" , "Small, short-bodied dog" .)