The possible reasons why a hamster doesn't eat may include the following:
Health Issues: A hamster may suffer from diseases such as wet tail syndrome, gastroenteritis, overgrown teeth, problems with the scent gland, or eye infections. All these will affect its appetite.

Environmental Changes: A new environment may make the hamster feel uneasy. Within the first week after it arrives at its new home, just make sure it has enough food and water, and occasionally check its physical condition. After a week, you can slowly lure it with food to let it gradually get familiar with your smell.
Food Problems: Spoiled, stale food or food that doesn't suit the hamster's taste will cause it to be reluctant to eat. Make sure to provide fresh and diverse food and avoid food residues.
Age Issues: As a hamster gets older, its appetite will gradually decrease, especially for senior hamsters.
Emotional Issues: A new environment or being frightened may make the hamster feel anxious and result in it not eating. You can cover the cage with a piece of cloth to create a dark environment and make it feel safe.
Methods and Measures to Deal with a Hamster Not Eating:
Seek Veterinary Examination: If you notice any abnormalities in the hamster, such as tears, red and swollen eyes, or obviously overgrown teeth, don't delay. Take it to the veterinarian immediately. Timely treatment is crucial.
Provide Fresh Food: Make sure to provide fresh food every day. Expired or spoiled food is a big no-no. Try to offer diverse food, including grains, nuts, fruits, and vegetables, to ensure a balanced diet.
Quiet Environment: A hamster needs a quiet environment to eat. Surrounding noise will make it feel uneasy. Try to place its cage in a relatively quiet place to reduce external interference.
Adapt to the New Environment: Within the first week after it arrives at its new home, just make sure it has enough food and water, and occasionally check its physical condition. After a week, you can slowly lure it with food to let it gradually get familiar with your smell.
Reduce Disturbance: Try to avoid disturbing the hamster excessively, especially when it is adapting to the new environment. Give it enough time and space to relax.
By taking the above measures, you can effectively deal with the problem of a hamster not eating and ensure that its health and nutritional needs are met.