My clock is slow over long period of time - Macbook Pro 2011 13"
The clock time is keep by a battery or capacitor on some models. It is a small battery on the motherboard and used when the computer is off.

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 &amp; 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.