One having a race with a “condition” — not well at finish (5-4)

'one' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'a race with a condition not well at finish' is the wordplay.
I cannot quite see how this works, but
'a' is present in the answer.
'with' could be 'w' (abbreviation) and 'w' is located in the answer.
'condition' could be 'term' (synonyms) and 'term' is found in the answer.
'not well' could be 'ill' ('ill' is the opposite to 'well') and 'ill' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'having' is the link.

Can you help me to learn more?