If there are no more official updates then by definition there is no official way.
So it's a matter of whether anyone has made a custom ROM for it based on a newer version of Android. If they have, and if a custom recovery also exists for this phone (both ROMs and recoveries are model-specific) then you can root the phone, install the recovery and use that to flash the ROM. Root methods are also model-specific, but something that old probably has enough vulnerabilities that at least one method exists. But I'd check whether a suitable ROM is available and works well before looking into the rest.
Since Android always has to be built for the device there is no "generic" update you can use and you cannot use an update (official or otherwise) intended for a different phone.