Leave the pet classes to new jobs such as the Ranger if it ever gets released or a wyvern for the dragoon.

I envision the summoner class to be able to dart in and out of close combat, deal direct damage to a foe whilst gaining Elemental Focus with each attack. Maybe you can choose which element to align to creating tactical play, choosing the right element to achieve the upper hand in the given situation .

Phasing/teleporting to give them the ability to get in the face of the enemy and deal damage and then out to then be able to actually Summon a Primal when the elemental focus has reached it's focal point.

The Summons themselves must be attained like they have been so far, with quests that make them feel like it was a hard slog but also very very rewarding. I would also like the amount of summons to be increased and for each Summon called forth to have a specific unique selling point.