Upon discovering sensitive information, such as high-profile celebrities' user accounts, the most appropriate and ethical next step is to immediately contact the client. This allows the client to take necessary actions to secure the data and mitigate any potential risks. It is important for a penetration tester to maintain confidentiality and integrity, and directly contacting the celebrities (option A), deleting the accounts (option B), or merely recording the findings without immediate notification (option D) would not be appropriate professional responses.