Line restraining stray dog (7)
I believe the answer is:
terrier
'dog' is the definition.
(terrier is a kind of dog)
'line restraining stray' is the wordplay.
'line' becomes 'tier' (tier is a kind of line**).
'restraining' is an insertion indicator.
'stray' becomes 'err' ('err' can be a synonym of 'stray').
'tier' enclosing 'err' is 'TERRIER'.
(Other definitions for terrier that I've seen before include "Reserve soldier" , "Breed of dog - volunteer soldier - estate register" , "Breed of dog - Territorial Army volunteer" , "See 11" , "Dog - army volunteer - land register" .)