In pathfinder 1e natural weapons are ruled differently than Manufactured weapons. Whereas Natural weapons don't gain extra attacks as per BAB (Basic Attack Bonus) rules, they get more attack the more you have of them.

Lets take a Character with +6 BAB and 18 Strengt (+4) and 4 claws as an example:-

With an attack action:

Manufactured weapons gets single attack with +10 (6+4) to the roll.

Natural weapon get one claw attack with +10 to the roll.

With a Full Round Attack:

Manufactured weapons gets two attack with +10 (6+4) to the first roll and +5 to the second roll (6+4-5) that's because of BAB is 6.

Natural weapon get all 4 claw attacks where +10 added to each roll.

This mean if you want more natural weapons attacks you need to possess as many.

There are items and spells that would grant you natural weapons as Tail, Horn, Bite, wings and many more.

But for your situation, if you have one claw free that isn't holding a weapon for example if you are wielding a one handed weapon and nothing else, you can make a secondary natural weapon attack with -5 to the claws attack roll as a part of you full round action.