I would say that a good case could be made that Ottoman dominance in Eastern Europe and Western Asia was causally important -- although certainly not the sole cause -- in both the Renaissance and the Age of Discovery.

The conquest of Constantinople lead to some important Greek scholars and such going west as refugees. This played some role in the renaissance interest in broad classical learning (not just "the parts of classical learning already incorporated into Medieval Western canon like Aristotle, Vegetius, etc.").

Ottoman dominance of the Eastern Mediterranean also was disruptive -- or at least onerous -- for old Silk Road trade routes of which the Venetians and Genoese had focused on being the westernmost relay. This lead to increased interest in trade routes beyond the Strait of Gibraltar -- and new more western powers such as Portugal and newly-unified Spain playing a greater role in finding routes, such as the route around Africa to India, and the failed attempt to find a route straight West to China which lead to the European discovery of the Americas.

This is not to say that Ottoman power was necessarily the most important factor in either the Age of Discovery or the Renaissance -- just that it is one of the common causal factors in both that comes to mind.