Русско-англо-русский юридический словарь

To file a claim, you should start by notifying the person or business you’re suing that you plan to file a claim against them. (Houston Chronicle)

He is now bringing an unfair dismissal claim against the company. (Cambridge Business English Dictionary)

To maintain an action or suit is to commence or institute it; the term imports the existence of a cause of action. (Law Dictionary)

In the common law, where the property of the goods has passed to the buyer under a contract of sale, and where the buyer wrongfully neglects or refuses to pay for the goods according to the contract, then the seller may maintain an action against the buyer for the price of the goods. (LexisNexis)