Currently have OS X El Capitan system. I need OS X version 10.2 or later. Can I upgrade my system?

10.12 is available here, How to upgrade to macOS Sierra - Apple Support

Any mac that can run 10.12 can upgrade to 10.13 High Sierra which still receives Security Updates,

How to upgrade to macOS High Sierra - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

If you mean Mac OS X 10.12 and your MacBook Pro is a mid-2010 or newer model, yes.

If you mean Mac OS X 10.12 and your MacBook Pro is an earlier model, no.

If you mean Mac OS X 10.2, neither it nor any software compatible with it can run outside of emulation on your Mac.

(178826)