Derelict hut -- his housing an unknown dog (4,3)
I believe the answer is:
shih-tzu
'dog' is the definition.
(Shih-Tzu is an example)
'derelict hut his housing an unknown' is the wordplay.
'derelict' is an anagram indicator (a derelict or broken spelling).
'housing' means one lot of letters goes inside another.
'an unknown' becomes 'z' (algebra).
'hut'+'his'='huthis'
'huthis' is an anagram of 'shihtu'.
'shihtu' enclosing 'z' is 'SHIH-TZU'.
(Other definitions for shih-tzu that I've seen before include "Dog with short legs and long silky hair" , "Breed of dog with long hair and short legs" , "Eastern dog breed" , "Short long-haired dog" , "Breed of short dog with long silky hair" .)