If I have an idea for a college team t-shirt design and I don't have a license, can I propose that design to a company that has that college team license and set up a contract with that company and have them sell the product (that must be approved by the college team I assume)?
If the company who has the license has sublicensing rights then the answer is yes. Otherwise, you will have to deal with the licensor directly.
This appears to be a sublicensing question. As a result, the answer will lie in the license contract that the company has. To answer your question, you need to find out if the company can sublicense to you, or in the alternative, you would have to have the company create the shirt and use their license by purchasing your idea and making it there own.
You can propose anything you want. However, as you have correctly deduced, any trademarked logos or artwork can only be manufactured and sold according to the contract(s) of the entity that owns the trademarks. if the team (Licensor) owns the trademark and has licensed that trademark to the company (Licensee), the the company is acting within the law. if you want to utilize the trademark in a design to be used by the company, then the proposal must meet the requirements of the Licensee/Licensor contract.
The only advice I can really give is that you need to hire an attorney. I am providing this post as a general statement related to a general question. Your case involves specific facts which have not been provided. You deserve complete answers which cannot be given through this forum. Please realize that until you sit down with an attorney and answer that attorney's specific questions regarding your case, you should not rely on any answers posted in this forum. This answer does not create an attorney client relationship.
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