Web search is your friend :-) I did a search for NAPCO P-1664 battery and found installation manuals, which then list the battery needed -- a small 12-volt lead-acid battery. Since there are several models of this alarm system I have not linked to a specific Web page.

Batteries of this type vary widely. You could remove the battery as far as it goes without disconnecting it and note (or photograph) the markings on it. Then you could go to a place that sells such systems (locksmith?) or to a store like Batteries Plus or go on-line for a similar battery.

But some company must be monitoring this system for you. It might be easiest to call them first and ask them if maintaining the hardware is part of your contract with them or what it might cost for them to send someone who could replace the battery with a new one and not mess up the system/lose settings/etc. in the process.