Well, one of the quests to complete after the main story is to face off against some of the tougher optional bosses. These bosses are much more difficult than the ones in the main story and offer great rewards upon defeat. There are also quests that revolve around rebuilding parts of the world. You might need to gather resources and help the local inhabitants to complete these quests. Additionally, there could be quests that are triggered by certain events or items that you only come across after finishing the main storyline.
After the God of War main story, you can do quests that involve helping the various non - playable characters you met along the way. There are often additional tasks they'll give you. Another type of quest could be related to collecting all the remaining artifacts or lore pieces in the game world. This not only gives you a more complete understanding of the game's lore but also might unlock some minor rewards. And don't forget about the combat - based challenges that often pop up post - main - story to test your skills with the fully - leveled Kratos.