No, it does not apply to your independent contractor: a contract only binds the parties who sign it, and your independent contractor is not a party to it. He or she, as the term "independent contractor" implies, an indepedent party.You can certainly require your independent contractor to sign an agreement obligating him or her to this non-compete--or to a general non-compete with your firm--if you like, as a condition of receiving additional work or contracts from you.