Famous Scandinavian's pet (5,4)
I believe the answer is:
great dane
'pet' is the definition.
(I've seen this before)
'famous scandinavian's' is the wordplay.
'famous' becomes 'great' (I've seen this in another clue).
'scandinavian' becomes 'dane' (person from Denmark).
'great'+'dane'='GREAT DANE'
(Other definitions for great dane that I've seen before include "Kierkegaard, perhaps?" , "Pet" , "A best friend" , "one among best friends" , "Big dog" .)