Pleasantvalley, Welcome to the PondBoss forum.
It sounds to me like you have an unusual, if not unique opportunity with your new property. Having a small pond apparently devoid of fish, and a stream with brookies and possible rainbows seems exceptional.

Does the stream with trout flow into or through the pond? If that's the case, pond water temps could be cool. If too cool, BG, LMB, and other warm water fish may not recruit well.

Bill Cody's suggestion of male BG and YP is likely a very good one for cool water. If your trout stream connects to the pond, the trout could use the pond part or all of the year and grow larger than if only in the stream.

Rather than sourcing male only BG, another consideration could be GSF. Experts could weigh in on this combo (GSF and YP). BG are disappearing from my cool water pond; GSF have persisted. I have no idea if the GSF tolerate cooler water than BG and that is why they are thriving.
GSF predation on the YP might advantageously keep the YP from overpopulating.

You may want to consider keeping the bottom clear of snags so that if things got too far out of whack, you could effectively drag a seine through the pond, or nuke it, and remove out the unwanted fishes.

I am no expert whatsoever on any of this. Just throwing out ideas that are in my head.