The clock time is keep by a battery or capacitor on some models (not the main one) but. It is a small onebattery on the motherboard and used when the computer is off. When
When the computer is on and online it will automatically update the clock time.
Normally that battery last 3-5 years.
Try setting the time manually, by getting the actual update for apple time server.
sudo ntpdate -u time.apple.com
then you will see something like
8 Jun 14:30:11 ntpdate[28267]: adjust time server 17.151.16.14 offset 0.000336 sec
You generally don’t need to do this if you use the “Set date and time automatically” feature within the Date & Time settings.
If that did not work, reset your SMC and PRAM (System management Controller)
I can not believe it is your battery but everything is possible :(. Assuming you do not have 2 left hands, you could do that your self.