Moonlighting a remote job while working at a public firm. Easy extra money or career suicide?

Okay so I'm not sure how this is going to sound but it's something that I would like to have a grasp on before I make a decision.

I currently work at a relatively small public firm (10-13 partners, 40-50 total employees) and am looking into finding a remote part-time position preparing simple tax returns. I am not trying to overload myself with work and stress, just something to make an extra $15k-20k during the tax season. My current position at the PA firm is all in-person so I would be looking to do about 15-25 hours per week at the remote position.

So, my question is, how frowned upon would this be if my firm found out that I was doing this? I am concerned that when I apply for the remote position, that they will contact my current firm due to resume references and such. Should I just straight up ask if this is an acceptable thing to do? Is this an absolute NO or something that is really not a big deal at all?