This answer assumes you have downloaded and installed all the available updates for Mavericks (OS X 10.9.5). The latest possible macOS available for your Mac is Big Sur. Apple provides the website How to download macOS which has the URL https://support.apple.com/en-us/HT211683. However if you use the version of Safari included with Mavericks to access this URL, you will instead get the following message.
A possible alternative would be to use the version of Safari included with Mavericks to access the website http://maclinks.publicvm.com. Here you will find links to the Apple App Store for High Sierra through Ventura. For example, the link for "Big Sur 11" will open the following App Store window.
If you have problems signing in to the App Store, then the question No input fields for the Apple ID Verification for the iMac 10.10.5 might provide some help.
I should also point out that Tetsujin's answer comes with the following warning.
If you are trying to jump a long way - say from 10.8 to 10.14 or later, received wisdom is to first upgrade to El Capitan 10.11, then High Sierra 10.13.
This will prepare your machine for the long jump.
Some users seem to have managed to skip El Capitan, but High Sierra is still necessary, if it or newer has never been on the Mac before, as it adds a firmware update required to read the newer APFS filesystem.
IMO, you might consider first upgrading to High Sierra, then upgrading to Big Sur. Although, when I tested in a virtual machine, I was able to upgrade from Maverick directly to Big Sur.