It is also possible that the new battery is defective. I had this happen once. As a test, I disconnected the battery and brought it up with a battery charger. I measured the voltage after I charged the battery and it measured 12.6 volts as it should. I left the battery cables disconnected and measured the voltage 3 hours later. It was just over 9 volts. I returned to the store where I bought the battery and they didn't have a replacement, so I got my money back and went to another store. The new battery solved the problem.
At any rate, an electrical system check is in order to be certain whether it is the alternator, the battery, or something pulling power when the car is parked.