Yes, you can. The main function of your gallbladder is to store bile, and releases some bile into the small intestine when you eat, where it goes on to break down fats. Without the gallbladder, your liver then releases bile straight into the small intestine, which allows you to still digest food.
It’s therefore advisable to avoid large amounts of foods high in fat and/or fibre, which can become harder to digest, which may result in issues such as bloating and diarrhoea.
Adjusting your diet after gallbladder removal therefore not only helps you to function as per normal, in fact, it may even increase your life expectancy. Maintaining a healthy diet and weight can help decrease risk of other health conditions such as heart problems, high blood pressure, diabetes, cancer and more. Consuming fewer calories in your daily diet can also help to improve your liver function by allowing your body to digest your food easily, and use energy even more efficiently.
In summary, you can live a normal life even without a gallbladder, and it typically doesn’t affect your life expectancy. The main thing to take note of would be your diet and lifestyle post-surgery, to help you live a longer and healthier life.