Dog has a drink taken outside, accordingly (5,4)
I believe the answer is:
lhasa apso
'dog' is the definition.
(Lhasa apso is an example)
'has a drink taken outside accordingly' is the wordplay.
'drink' becomes 'lap' (lapping is a kind of drinking**).
'taken outside' means one lot of letters goes inside another.
'accordingly' becomes 'so' ('so' can be a synonym of 'accordingly').
'has'+'a'='hasa'
'hasa' inserted within 'lap' is 'lhasaap'.
'lhasaap'+'so'='LHASA APSO'
(Other definitions for lhasa apso that I've seen before include "Shown [AT CRUFTS]" , "Tibetan breed of dog - a salsa hop (anag)" , "small dog" .)