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I got a DRRI the other day and while it gives me the tone I'm looking for, there's a high pitched hiss that is audible whenever I'm not playing. Would something like a noise gate kill the hiss?

Find out the source of the hiss first. Does the amp hiss with nothing plugged in? If it's the amp, a noise gate won't help. If it's the guitar or pedalboard, a noise gate would fix it, but depending on how high you have to set the threshold, it may chop off the tail end of your notes (the amp 'verb might mask this anyway). Check for any sources of interference in your signal path, and try to stop the hiss at the source before resorting to a noise gate.

The amp does not hiss when nothing is plugged in. My one spot hisses when it's plugged in so I'm going to switch power supplies but the hiss from that comes from the power supply and not the amp and it doesn't seem to add hiss to the amp. I should probably check my cables next

Yeah, a noise gate is never the answer for clean amp hiss unless you're running a high gain pedal setup that's causing the problem and you need to tame things to make it functional and/or bearable. The hiss you describe should be resolved through cable or power supply upgrades unless it's an issue with the amp itself which could be resolved by a knowledgable tech.

Is it new or used btw?

It's new. The amp isn't the source so I'll check cables and power supplies

Just plug straight in first thing, listen for hiss. As for pedals and cables, remove 'em one at a time to narrow down where the trouble is and go from there. You'll get it straightened out no problem after that.