The queen bee delivered with package bees has a good chance of dying during the first year. I suspect 50%+ package queens die within a few months of being added, leaving the new beekeeper queenless in the worst possible time. Typically, it is not the fault of the beekeeper, but a product of our industrialized beekeeping environment. While experienced beekeepers have the tools and knowledge to help the problem, new beeks are up a creek. New beekeepers turn to large operations who sell packages and queens in the tens of thousands. Unfortunately, these queens produced and shipped across the country have a high likelihood of failing. The solutions to the problem is to buy local when possible, but it's not always possible.
Queens sold in packages are mated queens; able to start laying fertilized worker bee eggs immediately. The package bee supplier is supposed to verify a queen has been fully mated and is laying eggs before being sold, but this does not always happen. A common practice is for large producers to sell queens without verifying they have fully mated. After mating, it can take a queen several days to start laying eggs. Instead of verifying a queen is fully mated before sale, large operations will often ship and replace a queen for free. It cost more money to verify a queen is laying fertilized eggs, than it does to replace the failed queens of the customers who actually notice. It's a money thing. Caveat emptor.
But, if you bought a package and your queen is nowhere to be found, these are your 5 options:
Buy a New Mated Queen
You can purchase another mated queen, even if from another supplier or type of honeybee. Often, the first call should be made to the business that sold you the original package to ask for a new queen. They will often ship replacement queens for free because they know there is a high probability a package queen will fail.
Introducing your mated queen to a queenless colony is the most common way for new beekeepers to fix the queenless problem. The new queen would successfully start laying eggs, but may soon fail or be rejected by the worker bees, much like the previous queen.
Buy a New Virgin Queen
A virgin queen bee is a queen that has not mated before sale. Virgin queens look nearly identical to mated queens, but are not able to lay fertilized eggs immediately. A virgin queen is released in the same way as mated queen, but will need to spend about a week going on mating flights before she will start laying fertilized eggs. A virgin queen has a higher likelihood of succeeding in the long term compared to adding a mated queen. This is because she will probably mate with more male bees and with males acclimated to your surrounding area.
Add a Frame of Very Young Brood from Another Hive
This options is available if you have another established hive. If you are a new beekeeper with two new packages, it is unlikely that the hive with a queen can afford to give up a frame of brood. It can certainly be done, but will jeopardize the health of the donor hive. Adding a frame of brood with eggs (without adult bees) to a queenless hive will give the queenless hive a chance to raise their own queen. Even if the eggs are from another hive, worker bees can feed royal jelly and grow the egg into a queen.
This method has the highest probability of long term success if a queen successfully hatches out. The more "ownership" a hive can have over raising its own queen, the more likely they are to accept her as their queen. But, this method will take the longest to complete, around 25 days until you have a replacement queen.
Add a Queen Cell from Another Hive
Occasionally, the timing works perfectly and another hive will be making queen cells the same time another hive is queenless. Beekeepers can take advantage of this by moving a capped queen cell from one hive and placing it in the queenless hive. The easiest way to do this is to move the entire frame (without adult bees) with a queen cell on it to the queenless hive. Be sure to not remove 100% of the queen cells from the donor hive and that there is at least one on another frame. Don't want Peter to go bankrupt so Paul can be paid.
This method has a high success rate, the same as allowing the bees to raise their own queen (but faster). If all the queen cells from the donor hive are on the same frame, you can carefully cut the capped queen cell (including about 1 inches of comb around the cell) from the donor frame and gently press it into the comb on the queenless hive.
Combine the Queenless Hive with Another Hive
Two hives can be combined into one hive easily and is sometimes all a beekeeper can do. It may be time to combine two hives if winter is coming and there isn't enough time for queenless hive to prepare for winter or all resources for requeening have been exhausted. Combining two hives is very simple, the easiest method to do it is the newspaper combine method.
It is almost fruitless to allow a failing queen or a queenless colony to go into winter. Hives in these conditions cannot survive the cold nights of winter, starving long before dandelions break the ground in the spring. But, a beekeeper can learn a lot from letting a weak hive go into winter. It can help you get a baseline for the minimum population needed to survive the winter. It can also give you an idea of how long a weak colony can survive and how much honey they eat. Learning what doesn't work is just as valuable as learning what does.
Local beekeepers are unable to meet the demands of their beekeeper friends. Because there is such a high demand for bees, the majority of new beekeepers buy their package bees from very efficient, industrialized queen breeding apiaries. While efficient, the volume of bees and queens produced are typically not up to the quality needed for bees to survive in our difficult climate.
We spend a lot of time every year helping new beekeepers who buy packages, who are left queenless within a couple months of starting. If planning on starting beekeeping, the single best thing you can do is buy/reserve a nucleus colony from a local beekeeper. This will solve most of the problems you could run into during your first year. Don't postpone, it is extremely difficult to find a nucleus hive in the spring that has not already been spoken for.