Can you drink alcohol a week after having your gallbladder removed, currently taking no medication?

If everything is well and no pregnancy, if you are healthy, 1 week after gallbladder surgery, it is safe to drink alcohol. It is not safe to drink more than 1 drink a day (for women, in general) and there is debate if any amount of alcohol is safe (in general).

No. Alcohol is a poison that never did anybody any good, ever, so stay away from it. It will destroy your brain cells, facilitate development of cancer in many organs,including breast, cause hepatitis, cirrhosis and pancreatitis etc. There is no safe level of alcohol intake. Quit while you are ahead.