There exist hormone implants that pause the egg laying in birds. The drug is called Deslorelin (brand name Suprelorin) and is implanted subcutaneously similar to a dog’s microchip. It’s used to help with the treatment reproductive diseases like prolapse, egg binding, and internal laying.
We’ve been using it with Summer, one of our hens who was diagnosed with a reproductive cancer. The implant doesn’t treat the cancer but slows it down considerably.
More information in this article from Poultry DVM.