Dog also has a pee when tickled (5,4)
I believe the answer is:
lhasa apso
'dog' is the definition.
(Lhasa apso is an example)
'also has a pee when tickled' is the wordplay.
'pee' becomes 'p'.
'when tickled' is an anagram indicator (letters tickled out of place).
'also'+'has'+'a'+'p'='alsohasap'
'alsohasap' anagrammed gives '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" .)