There's currently only four tabs in the iOS app's "top" site view, meaning you still have an open slot.
I suggest that something akin to the web site's "front page" be added there. This would probably be a list of questions selected for their recent activity and interesting-osity® to the user, based on the usual stuff like that user's favorite/most frequent tags.
On Stack Overflow, the raw "questions" list is all but useless due to volume and range of subjects. I frequently pop over to the front page to get a more curated view of new stuff, and more often than not stumble across something worth looking at, even if that's just because it's mis-tagged. On a smaller site, the front page gives a good overview of recent activity, and, via favorites highlighting, attracts one's attention to questions one might have missed but want to interact with.
I don't think this needs to be a copy of the web site's functionality, but something in the same spirit: a slightly serendipitous filtered version of a broader view than a single tag's question list.