The phrase "to start the proceedings" means to begin or initiate the official actions or proceedings of a meeting, event, or legal case. Full definition
If your spouse starts proceedings in one country, you may not be able to initiate them in another. (irwinmitchell.com)
Starting proceedings doesn't mean that your claim will definitely go to trial. (irwinmitchell.com)
Another aim of the proposed directive is to give the victims sufficient time to start proceedings after an infringement occurred or after the victims became aware of an infringement of antitrust law. (europeanlawblog.eu)