Guilfordbeekeepers.org

First time beekeeper. I installed a nuc Sat. a week ago. Inspected this past Sat.
A lot of activity. Not sure about eggs, hard for me to spot for sure but lots of larvae and capped brood.
I did see the queen which is last year's queen.
Of 3 new frames, they were drawing out comb on 1 fairly well. Not much activity at all on last two.
My concern is looks like two queen cups built. They looked empty.
Should I add super or leave another week?

I don't know if you are using 8 or 10 frame equipment, but if all but 2 of the frames have been drawn out, move the 2 undrawn frames to the edge of the brood area (to encourage the bees to draw them out and to expand the brood area), and add another super. If you put a new super on too soon, the bees will build upwards (chimney) and not draw out the outer frames.

If you are not seeing royal jelly in the queen cups, you don't need to be overly concerned. Bees will build them even without a present intent to use them. Some bees build more cups than others.

Welcome to the forum. It would help if you post your location (town, city, county). We don't restrict who joins, but since all beekeeping is local, and sometimes what is happening with the bees can be very localized, it helps to know.