Guide by Nikolai from PN Forum
When your pet's hunger level reaches the maximum (the hunger level bar is all green), you are able to 'discover' a skill! The 'discover' buttons in the Pet Kennel window will be colored orange which means you can discover a skill. If all your pet skill slots are full in a row and you try to discover a skill, the system will choose a random skill slot in that row and replace it with a random skill.
Pet Skill Lock
In the Item Mall. you can buy an item called [Pet Skill Lock] (28 gold/gift coupons) which will lock only one skill of each type, at a time. This is useful when you have filled up all the open skill slots with skills. Like I said above, if you discover again with a row of full skill slots, it'll take a random skill slot and replace it with a random one. If you lock a skill (click on skill in Pet Kennel and choose Lock, must have [Pet Skill Lock] in bag), it will not be replaced.