Star carrying animal to old Japanese dictator (6)
I believe the answer is:
shogun
'old japanese dictator' is the definition.
(historical term for a Japanese military leader)
'star carrying animal' is the wordplay.
'star' becomes 'sun' (the Sun is a star).
'carrying' indicates putting letters inside.
'animal' becomes 'hog' (hog is a kind of animal).
'sun' enclosing 'hog' is 'SHOGUN'.
'to' is the link.
(Other definitions for shogun that I've seen before include "Hereditary Japanese military governor" , "Former military governor of Japan" , "So hung about with old Japanese army commander" , "Heredity commander of Japanese army" , "Hereditary military dictator of Japan until 1868" .)