The first thing that you need to determine when looking to replace an existing LED driver is to determine if the driver is a constant current or constant voltage. Many manufacturers such as the Thomas Research Products driver pictured below will state right on the label which they are.
If you are replacing a constant current driver, make sure the current is identical on the new driver. You will also want to make sure the power rating and efficiency is equal or higher, and the voltage output window is the same or similar.
If you are replacing a constant voltage driver, make sure the voltage is identical on the new driver. You will also want to make sure the power rating, efficiency, and the output current is equal or higher.
If the driver is dimmable, make sure you are getting the correct dimming style as there are multiple dimmable types.
Some other notes to keep in mind are the input voltage, IP ratings (resistance to dust or water), size, and termination style.