how long will macbook pro late 2013 be supported?

This laptop is now considered "Obsolete" by Apple so there is no more official hardware repairs.

However, the laptop does support the just released macOS 11.2.1 Big Sur which will continue to be have security updates until late 2022. I would Big Sur will be the last version of macOS to be supported on this laptop, but only time will tell when Apple releases the next major version of macOS in late 2021.

Even when the laptop and OS are no longer officially supported you can still continue to use the laptop. It is even possible to install Linux on this laptop to further extend the life of the laptop once Apple stops providing security updates to macOS. But this does require learning a new OS and you may find some apps and accessories are not supported by Linux.