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

Environmental changes: A new environment may make the hamster feel uneasy. In 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 scent.
Food problems: Spoiled, stale, or unappealing food to the hamster will cause it to refuse to eat. Ensure to provide fresh and diverse food, and avoid food residues.
Age issues: As the hamster gets older, its appetite will gradually decrease, especially for senior hamsters.
Emotional problems: A new environment or being frightened can make the hamster anxious and lead to it not eating. You can cover the cage with a cloth to create a dark environment, making it feel safe.
Methods and measures to deal with a hamster that doesn't eat:
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 a variety of foods, including grains, nuts, fruits, and vegetables, to ensure a balanced diet.
Quiet environment: Hamsters need a quiet environment to eat. Surrounding noise will make them feel uneasy. Try to place its cage in a relatively quiet place to reduce external interference.
Adapt to the new environment: In 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 scent.
Reduce disturbances: Try to avoid disturbing the hamster too much, 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.