The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.
With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. For Best results use Safari to commence the download as Others may not work.
Believe this computer may Qualify for the latest version of macOS Monterey
Safari will open a redirect and open the Apple Store where the download can commence
One may consider upGrading to High Sierra first if considering upgrading to any version above High Sierra. This may better position the computer for a possible Drive Conversion to the newer APFS format as well as any EFI BOOT ROM required to use the newer file format.
Tips Big Sir Upgrade Released Nov 2020
Tips Monterey Upgrade Released Oct 25, 2021
Make Time Machine Backup is very useful and can be used to Revert to Previous Working macOS
Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.
Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.
Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation
