Mean policeman with attitude to race? (6,8)

'race?' is the definition.
Both the definition and answer are singular nouns.
Perhaps there's an association between them I don't understand?

'mean policeman with attitude' is the wordplay.
I cannot quite understand how this works, but
'mean' could be 'middle' (I've seen this in another clue) and 'middle' is present in the answer.
'policeman' could be 'di' (detective inspector) and 'di' is found within the answer.
'attitude' could be 'stance' (stance is a kind of attitude) and 'stance' is located in the answer.
No letters remain.
This explanation may well be incorrect...

'to' acts as a link.

Can you help me to learn more?