* Clay is a noun acting as an adjective modifying "courts". It tells us what kind of courts we're talking about.
* Tennis is a noun acting as an adjective modifying "shoes". It tells us what kind of shoes are needed.
* Traction is a noun acting as an adjective modifying "shoes". It tells us why the shoes are needed (for their traction).
There are no proper nouns in this sentence. A proper noun is a specific name of a person, place, or thing (e.g., John, London, Apple).