I have OS-High Sierra ver. 10.13.8 and Safari 13.1.2 how can I upgrade? My iMac is later 2011.

There is no late 2011 iMac and there is no version 10.13.8. The closest to that is mid 2011 and 10.13.6.

A mid 2011 iMac cannot upgrade beyond High Sierra 10.13.6. See the following from Identify your iMac model - Apple Support

iMac (21.5-inch, Mid 2011)

Model Identifier: iMac12,1

Part Number: MC309xx/A, MC812xx/A

Latest compatible operating system: macOS High Sierra 10.13.6

For security reasons you should consider using a 3rd party internet browser that supports running a current version on High Sierra rather than using Safari. Two examples that will run their current version on High Sierra are Chrome and Firefox.

That is the highest OS you can go on a 2011 Mac, but...

Mostly you just need a more modern Browser than Safari on Mojave, or High Sierra like Firefox or Brave.

https://brave.com/

Thanks to dialabrain…

FWIW, Firefox 109.0 (current version) runs in High Sierra.

https://www.mozilla.org/en-US/firefox/new/