(phrasal verb) to start or commence a process in a court or before a judicial officer.
"If you do not make full payment by the 24th of May, my client has instructed me to bring legal proceedings to recover his claim."
Other forms
file proceedings (phrasal verb) to deliver to the court or other decision making body, the documents or pleadings relevant to a particular case. "I have a final meeting with my client this morning after which we will go to court to file proceedings."
commence proceedings (phrasal verb) to start a process in court. "As we have failed to reach a settlement with the other party, we have no choice but to commence proceedings."
institute proceedings (phrasal verb) to commence an action by filing proceedings. "After the documents have been filed, the other party will be informed that we have instituted proceedings."
discontinue proceedings (phrasal verb) to terminate a process that has been brought before a court. "The claimant decided to discontinue proceedings when it became clear that he could not win the case."
Source: Translegal