Short Answer: No
Long Answer: On older computers, you used to need to download a third party1 anti-virus software. On modern computers, the pre-installed programs are very capable and can replace paid and free third party software of the past.
On a Windows computer, the default Microsoft anti-virus program that comes pre-installed on your computer is very good and free. It will keep itself up to date and run automatic scans without you having to do anything. You can also run a scan manually.
On an Apple computer you generally don’t need any anti-virus software as most virus are written for Windows computers (the largest user base worldwide) and are .exe files, which cannot be opened on a Mac.
The only other program you might want to download both on Windows and Apple when it comes to computer security is Malwarebytes, which offers free and paid options.
Malwarebytes is is an anti-malware software for Microsoft Windows, macOS, Chrome OS, Android, and iOS that finds and removes malware. Made by Malwarebytes Corporation, it was first released in January 2006. It is available in a free version, which scans for and removes malware when started manually, and a paid version, which additionally provides scheduled scans, real-time protection and a flash-memory scanner.Wikipedia
- Third-party software is a computer program created or developed by a different company than the one that developed the computer’s operating system. For example, any software running on a Microsoft computer that was not created by Microsoft is third-party software.