Yes, you may have scars after cosmetic surgery. But while no scars disappear completely, they can become less and less visible over time. 

Scars happen after cosmetic surgery because the procedures typically involve incisions in the skin, and any injury to the skin will result in visible scars. The scar should look better as soon as the stitches come out, about a week after surgery, but it may take a year or more for the new scar to flatten and fade to match the surrounding skin.