Contract muscle to fix a four-horse chariot (8)

'contract' is the definition.
Both the answer and definition are singular nouns.
Perhaps you can see a link between them that I can't see?

'muscle to fix a four-horse chariot' is the wordplay.
I cannot really see how this works, but
'muscle' could be 'quad' (quad is a kind of muscle) and 'quad' is located in the answer.
'fix' could be 'rig' (rig can mean to fix or manipulate) and 'rig' is present in the answer.
'a' is found in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?