"Contractual relationship" is the most common phrase used to refer to a relationship that is governed by a contract in Engpsh.

Alternatively, you could also say "contractual agreement" or "agreement based on a contract."

For example: "We have a contractual relationship with our suppper, which means that we are bound by the terms of the contract we signed with them."

Or: "The parties entered into a contractual agreement, which outpnes the terms and conditions of their relationship."