Anything that is related to a pet in the game is usually done via the Animal Trainer NPC. The animal trainer can do many things, and when you become more experienced in the use of pets, you will find yourself often taking a visit to the Animal Trainer for one reason or another.
The Animal Trainer is an NPC that can be found in Randol or Dratan. Talking to the

Animal Trainer will open a menu. This menu is where you will be able to train, unseal (revive from the dead), harvest, or reset the
skills of your pet. You can also make Knightmare armor or Dragon
weapons using pet components via this menu.
1. Pet Training -
From this section, you can upgrade your armor - defensively or offensive, magical attack or magical defense. The max for each skill is level 20. For example, once you have reached level 20 on armor defensive, the window disappears as you have maxed it. Same for other skills. In this section, you can also get other minor horse skills like laughing (I think) which has no real value except to make your pet move as you want.
2. Mount Training -
Here you can make your pet horse or dragon a mount starting at level 31. BUT if you do at a low level, it will cost you to "unmount" your mounted pet, if you should decided to level it some more. Once a pet is mounted, they can gain no more levels. That is why I suggest to mount your horse at level 37, at which time, you can get the max buff of 10/10. (defense/offense). You can buff your self, or if you are in a party, then when you buff, everyone gets the same buff as you. Dragons have a max level of level 33 for their offensive skills now.
3. Harvest Pet Component -
This is how you get those dragon or horse parts. This is how I do it and it explains the process too. I get about 30 eggs and 30 panflutes. I go to Lorraine and get two quests. Go to Jajan in Dratan to get the two pet quests done. I can either use the animal trainer in Dratan or the one in Randol to sacrifice or "harvest" the pets. This is also called "saccing." I teleport to the animal trainer in Dratan. I equip the level 1 pet and click the Harvest Pet Component. Then another window pops up to ask if you are sure you want to havest the pet component. You say yes, and then you either fail or gain a component. Remember, this process is not easy.
The first time, I used this process, on the 6th trip i got a horse component. Then the next 50 trips nothing. You can use all horse or dragon pets. This is up to you now.
After harvesting the pet to the Dratan animal trainer, i teleport to the Dratan teleported and go back to Randol. Then I start the whole process all over again.
You can adjust the technique now. When you arrive in Dratan, you can teleport or walk to Jajan. Then you can teleport back to the teleporter. When you arrive in Randol, you can use the pet trainer there to sac your pets. Then off to Lorraine to start the cycle over again. You can do what you want now, but I just try to give you options now.
You can get any amount of eggs or panflutes to start off with. When you do get a part, go to S1 to see what the part sells for. You hit the jackpot if you get a tendon now. Save the eggs and panflutes for when you get bored and do say, 15 minutes of saccing (harvesting). I do suggest one thing. Do the saccing with a new character. The reason is, I have heard too many stories of people saccing their pet by accident. If you do it with a new character you do not have to worry about this.
4. Make Unique Armor or Weapon -
Note you can see the components to make any class of dragon weapon, but you can only see the components you need to make horse armor for your class only. You can only make a dragon weapon or horse armor for your class character only. You can not make another class of weapon or armor. And yes, the parts are expensive. Try to collect B parts as those have a slight % of succeeding. Try to make dragon weapon or horse armor is not guaranteed now. So if you fail do not be set back, but try again. Like upgrading with HS, do it late at knight on a slow server now.5. Release Sealed Pet -
This is simply the way to bring your dead pet back to life. When you click this a window appears. In this window is a square, in which, you drag the icon of your dead pet from your inventory. It will then tell you how much to unseal your pet under the window in which your pet icon is in.
Your pet window may say "17 hours till revival" and that is real time now. Yes, you would have to play 17 hours to unseal your pet for free. But if you play, say 8 hours, and it says 9 hours till revival, you still have to pay the full price. Yes, no discounts at reviving your pet now. lol
6. Reset Pet Skills - There are times you may need to reset pet skills. If you decide to trade or sell your pet you need to reset your pet skills. You may reset them to say magical defense if you are going on a demon party. Or set them to full armor defense for your pet trainer. There are numerous reasons why you may reset your pet skills. But you reset them for the situation that you are in and set them to what YOU think best.