I can not update my mac. There is no update button under the apple

The model year of a MacBook Pro is available at Apple menu > About This Mac.

A mid-2010 through late-2011 MacBook Pro can be upgraded to High Sierra 10.13.6 but no later version.

A mid-2012 through early-2013 MacBook Pro can be upgraded to Catalina 10.15.7. See: https://support.apple.com/en-us/HT211683

A late-2013 or later can be upgraded to the current version of Big Sur. See: https://support.apple.com/en-us/HT201475

See the following article:

https://support.apple.com/en-us/HT201541