How do I delete a previous google play game account on ClashRoyale

[AC Question]

Ok, so a long time ago I started playing clash royale and saved my really low level account to google play. I then started playing clash royale and made a new account not connected to google play. This account that is not connected to google play became very good and was a high level. I just got a new phone and want to move my account that is not saved on my google play account to this new phone. Whenever I play clash royale and try to sign into google play, it asks if i want to play with my old low level account. I want to play with my better account and save it to google play. I dont know how to delete this old account. I want to save my better account to google play. I have a lg optimus l90. please help. Thanks!!!