There have several types of pet skills that are used in Dragon Oath, but some more info about pet skills would be useful. First off, there are 2 types of skills: manual and auto. Currently, pets can only have one manual skill. This skill is activated by the master by clicking on it on the hotkey bar. All the other skills are auto skills that are cast by the pets themselves.

Manual ones will obviously replace the previous manual skill when teaching pet skills(buy dragon oath gold). However, it has a chance to lose any of auto skills it currently has for any other skill when you teach a pet a new skill . This makes teaching skills a risky endeavor and can be really costly, especially if good skills get replaced by other good skills. On the plus side, if you manage to get all the skills on your pet that you want to be on there, adding adv skills will just replace the old non-adv one. So start teaching new skills to your pet by using normal skills first then adv ones.

Pets generally stop learning new skills by themselves around 50-60. however there have a pet learn a new skill at L84 and it can get taught a new skill at L89. So anything is possible though the chances are very small. So you can try to get a pet to learn new skills at lower levels(Dragon Oath powerleveling) versus higher ones.