Every club in Golf Clash has it's own Club Card.
In order to unlock a new Club you will need to either find the Club Card in a Chest or purchase it from the store.  You can iderntify the rarity of a golf club by looking at the colour of the club card border. There are 3 club card classifications:  
Common (Blue)
Rare (Orange)
Epic  (Pink)
Don't worry if you find the same Club Card more than once as Club Cards can also be used to upgrade your Clubs.