"To open an investigation" means to begin looking into a situation or event, usually for the purpose of gathering information, finding out what happened, and potentially discovering any wrongdoing or solving a problem. Full definition
After the initial spending reports were delivered, the commission opened investigations into both leave campaigners over failure to submit sufficient invoices and receipts to document their spending. (theguardian.com)
The insurance company will then open an investigation of your claim. (nylawnet.com)
Your insurance company will then open an investigation and process your claim. (thecollegeinvestor.com)