Posts Visible to Members First

How can I make it so posts are visible for paid members for a day (or a set timeframe) before becoming publicly visible?

I’m putting together a site with Paid Members Pro (open to considering something similar) and would like to offer paid members the ability to post, as well as offer exclusive first-look access to the content posted by other members. But I’ve yet to find any plugins or info on how to make this a happen.