No, there will not be paid DLC between major expansions. The new model is:
The Destiny live team, which has been responsible for the patches and updates so far, has been bolstered with a team to create actual content, not just update features. The cosmetics store will fund that through the next (probably paid) expansion.
From what we know now, you won't be spending money for content in Destiny until next year's release. Among the benefits of this approach is, it keeps everyone on the same content base. It also means the team can manage their content release windows differently, and not be in perpetual crunch on the next DLC window.
The other advantage this gives the players is time. If they want us to have diversify our loadouts and optimize, we need time to get gear, to find different playstyles, to get that drop we want. We need time to complete the quests. A new expansion every 3-5 months was brutal on Bungie, I'm sure, but it also was a crunch for players. Every 3-5 months all your gear is invalidated. I'm sure I'm not the only one who felt harried to get it all done. Get to max level. Get that loot. Check those boxes. Now we can breathe.
I bet Hard Raid won't come til November. And then in a month, the Warpriest Challenge, followed by the Golgoroth Challenge, etc.
I also think that as a community, we don't want another Year One-style DLC, which did have its merits. It wasn't up to Bungie's Standards. DLC1 had a mediocre campaign & was super-short. DLC2 didn't even have a raid, and Prison of Elders went stale so fast I started getting into Crucible. Me. Getting into PvP. Madness. (It turned out to be a good thing).
A yearly (or a tick-tock big fall/small spring) DLC with periodic Queen's Wrath-styled events, Raid Challenges, Crucible Maps, Seasonal Vendors, whatever else they dream up. That sounds great.