How to store red bean paste?
As a fermented bean paste, it should last for weeks in an airtight container in the fridge. For best results, make sure to leave as little head room (for air) as possible in the container.

To be honest, when I store Miso (for example), I just squeeze the air out and put a clip on the bag it came in, and then leave it in the fridge.

If you need longer storage than several weeks, you can probably freeze it, though at that point you might want to consider buying smaller packages.