contract with (someone or something)
To agree with someone or a group to do something. No one on our staff has the time to scan all of those documents, so we'll contract with a company that can do it for us.
contract with someone (for something)
and contract (with someone) for somethingto make an agreement with someone to produce or supply something, or to do something. I will have to contract with an expert for that part of the project. We contracted with a local builder for a new kitchen. Did you contract for plumbing work with Eric?