Can an opamp have its own voltage regulator?
Assuming you're using the opamp in a feedback configuration circuit, which you probably do because you need some precision.

Also assuming that the voltages at inputs and output of the opamp do not exceed what the opamp can handle at the given battery supply voltage. I'm thinking (common mode) input voltage range and output voltage range with a certain load connected.

Then the battery voltage drift should be irrelevant.

In a properly designed circuit the gain (and offset) of the opamp will then determine the output voltage, not the supply voltage.

So yes, you can add a regulator but I don't think you have any reason to do so. It will only use up some of the battery voltage (and power) while perhaps not improving anything.

What you might need is a "low battery" detection and indicator (for example, a flashing LED) to indicate that the battery voltage has become too low and accuracy might be compromised.