The Ingram Suspension is Big. Who fills the role?

I'm not convinced Kamara can do it (and going by SP's words not sure he does either). Edmunds/Williams/West seem to be the front runners to try. At this point I'm honestly not sure. I'm expecting to see more use of the passing game, particularly in the red zone, these first four games.
I agree. For those who missed what Payton had to say about this topic:
"The mistake would be that Alvin gets 15 more carries," Saints coach Sean Payton said on Saturday at the team's rookie minicamp. "That's not the direction we would expect to go."
Don't expect extra work for Alvin Kamara in Mark Ingram's place; that'd be 'the mistake,' Sean Payton says

That is pretty clear to me. Don't expect Kamara to pick up Ingram's load. Payton will rely on other RBs or maybe an increase in the short passing game.