You have 3 missions for the summer:
1. Look for signs the bees are rejecting the queen, and support them during this process of queen replacement;
2. Keep up with the growth, including with getting honey supers drawn out in July and August,
and support it, with feeding and with giving more space on time;
3. And look for signs that the bees are preparing to swarm.
At the very beginning of your journey with the bees, it's a good idea to treat for mites. One option is to use
Apivar strips - 2 of them - to mop up any mites that came along for the ride.
If you can test for mites, you check in August to see if you need to treat. If you can't, instructions below for treatment options.
Below is a comb with a 2 week old queen on it, and a supercedure cell. It's from a mating nuc, where for some reason known only to the bees this queen was judged unacceptable. I cut out the queen cell, but they superceded her later anyways. I've come to the conclusion that the bees are a better judge of queen quality than I am. ABout 10-15% of queens from a package are either rejected immediately or rejected eventually. This could be due to poor weather when the queen was mated in March in the South, or due to shipping conditions damaging the queen. Trust the bees, they're trying to fix it!
Why is a supercedure event a risk for the hive? Unfortunately, sometimes the only virgin queen that departs for her mating flight doesn't make it back. Bees don't think in terms of "plan B". Instead, it's one queen to rule them all.