How to upgrade Mac from macOS Sierra to OS 11?

The "here" link that Niel posted is to an Apple Support article.

How to download and install macOS – Apple Support

It will not make your Mac accept a newer OS. Your Mac will only install whatever versions of Mac OS X / macOS are compatible with it. So if you try to install macOS 13 (Ventura), or later, your Mac will block the installation at some point.

However, you indicated that "i need it [the Mac] to have at least os 11."

Which means that if you access this Support article from your Mac, you can use the "Big Sur 11" link to get the installer for macOS 11 (Big Sur) – or the "Monterey 12" link to get the installer for macOS 12 (Monterey). Those two versions of macOS are compatible with your Mac, so you should be able to use either of these links.

I would suggest installing Monterey.

Back up your data, check the application compatibility table, click here, and then on the download link for a newer OS. Its maximum one is Monterey.

Catalina and above won't run 32-bit software and split the functions of iTunes up; if you choose one of them, use Go64 as well.

(262960)

Another way to get a macOS installer might be to run the App Store on your Mac, do a search for "macOS", and click on the Story "Download macOS Versions".

The ability to get old versions of macOS in the App Store directly, without going through the Support article, is a fairly recent change. Apple used to make the App Store hide old versions of macOS, so you had to know about the Support article to be able to get them.

Whether you go through the Support article, or the "Download macOS Versions" story, you will get the same Big Sur or Monterey installer.

Note that neither Big Sur or Monterey are among the "most recent three" that receive love from vendors such as Microsoft and Adobe.

While their versions of Safari are much newer than the one in Sierra, neither receive the most recent versions of Safari.

Either is enough to run

• The current version of the Firefox Web browser
• The LibreOffice office suite
• The parts of Affinity Studio that are "free with registration." (AI stuff that requires a paid subscription requires an Apple-Silicon-based Mac running Ventura or later.)

Monterey is enough to run

• The current versions of most other major third-party Web browsers (such as Brave, Opera, Google Chrome, and Microsoft Edge)