There should be a process in the contract itself on how to deal with contract disputes. Failing that, the contract should be followed as is, so if your supplier decides to raise the prices then you should discuss the unexplained raise in prices with your supplier first, and then decide on your course action. Note that it is legal for you to get out of the contract and to sue your supplier. But, of course, you should take the best interests of your project and your organization into consideration. Can you afford to switch supplier at this very moment? Are other suppliers providing cheaper prices? Is the current supplier reliable when it comes to on-time delivery and material quality? Pondering these questions and answering them honestly (in other words, taking your ego out of your equation) should guide you on what you should do!
To answer your last question, yes, contract disputes fall under conflict management. Conflict management encapsulates suppliers, vendors, stakeholders, and team members.