Old King ate 51st dog (6)
I believe the answer is:
collie
'dog' is the definition.
(collie is a kind of dog)
'old king ate 51st' is the wordplay.
'old king' becomes 'cole' (nursery rhyme character Old King Cole).
'ate' is an insertion indicator.
'5lst' becomes 'li' (I can't explain this - if you can you should give a lot more credence to this answer).
'cole' enclosing 'li' is 'COLLIE'.
Can you help me to learn more?
(Other definitions for collie that I've seen before include "Popular sheepdog like Lassie" , "Scottish sheep dog" , "Type of sheepdog" , "Sheepdog wth ling nose and shaggy hair" , "Long-haired intelligent dog" .)