I think I have laying workers - can I add a new queen?

If a colony of bees is queenless for long enough and they have no brood of any sort left in the hive, then workers can start to lay eggs in the cells themselves. These are unfertilised eggs so will not be of any use for the colony. Unfortunately, by the time you get to that stage in a colony, it really is not worth trying to safe them. The remaining bees will very rarely accept a new queen being introduced into the hive, they will instantly kill her. The best method is to move the hive off the stand and then shake out all the bees from the frames and let them drift into your other nearby hives. You can then clean up the frames and hive and repopulate it with a new swarm, a split from another hive, or purchase a nuc of bees.

A colony with laying workers often has multiple eggs per cell, rather than the usual one:

However, don't be fooled! a newly mated queen, with all her excitement and vigour can also lay multiple eggs per cell when she first starts off. however, she will soon calm down and find her proper laying pattern soon enough.

laying workers will also produce a very irregular pattern with 'drones' being laid in the smaller worker cells.