I have a hive that might have a queen, but I cannot find her. This hive is from a removal/cutout. I did not think I got the queen, but gave them some time. There is brood present, but most of it looks older. Not much new, if any.
Since I am not sure, can I still drop in a frame of eggs from another strong hive? I would like to do this before one of the workers starts to lay, or something. If I am on the right track, the frame needs to have the tiny egg, standing on end, to be potential.
I just want to get ahead of the game a little.
You are on the right track. Put a frame of eggs in the hive. If they don't have a queen they can use it to make one. You can check the frame after about 4 days to see if they are making queen cells. I did this about 10 days ago with a hive I split. Try as I would, I could never find the queen, but there were multiple queen cells that I left in the hive of origin (capped brood, larvae, but no eggs visible). I wanted to find the queen and put her in the new split. Having failed at this, I put a frame of eggs from a good hive in the new split. There are now 2 queen cells that had larvae in them when I checked 4 days after putting the frame in the hive. The original hive has not swarmed yet, but I still expect them to. More information than you wanted or needed, but I wanted to let you know that I did exactly what you suggested, but for a different reason.