contract something out
to make an agreement with someone to do a specific amount of work. (Rather than doing it oneself or in one's own place of business.) I will contract this out and have it done by consultants. I contracted out this kind of job the last time.
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?
put a contract out on someone
[for an underworld character] to order someone to kill someone else. The mob put out a contract on some crook from Detroit.