New hybrid battery. How often do I need to drive?

If you're buying a new from the dealer OEM replacement, you'll be fine. But do drive it around or keep it 'ready' to maintain the 12v battery.

 

NO. The HV battery doesn't much care now often or how little it is used.
The 12 V does though.

 

There are plenty of reasons including your batteries to warm up and drive the car every 7-14 days. You want to avoid flat spotting your tires, reduce excessive rotor rust, lubricate the top of the engine, exercise seals especially brakes & ac, circulate the coolant systems, etc.

 

YES. But a "drive" of less than 5 minutes doesn't really count.
30 minutes total "ON" time or more to properly exercise everything.