At any given time during your journey, you can stop for a moment in order to bring up a menu that will allow you to interact with your Starter Partner Pokemon. This interaction is very similar to what players could do in both Pokemon Amie and Pokemon Refresh in previous Mainstream Pokemon Games, allowing you to feed and pet your Starter Partner Pokemon.
When bonding with your Starter Partner Pokemon in this manner, they will have a happy aura appear around them should they be enjoying the snack you give them or where you pet them. This will increase their affection towards your trainer, which can give them special boosts in battle that includes higher Critical Hits odds, higher Partner Power chances, removing Status Conditions naturally, and holding on from attacks with one Hit Point remaining. Furthermore, the happier your Starter Partner Pokemon is with your trainer, the higher their Stats will be increased (by up to 10%).