Dish races off around a state with a youth (6,5)
I believe the answer is:
caesar salad
'dish' is the definition.
(Caesar salad is an example)
'around a state with a youth' is the wordplay.
'around' indicates putting letters inside.
'state with' becomes 'caesars' (I can't explain this - if you can you should give a lot more credence to this answer).
'a youth' becomes 'lad' (lad means a young man).
'caesars'+'lad'='caesarslad'
'a' put within 'caesarslad' is 'CAESAR SALAD'.
'races off' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for caesar salad that I've seen before include "leaves meal - with 14a" , "Dish of dressed lettuce with croutons" , "Dish containing lettuce" , "Lettuce-based dish" , "Course supplement" .)