Semolina flour has a long expiry date if it’s stored in a cool dry place. So the answer to this question is it depends. It depends on if your pantry is always cool and dry then it’ll be fine in at room temperature until the expiry date on the package.  If instead you’re like me live in a hot, humid climate then the refrigerator or the freezer is the best place for semolina flour. I like to transfer semolina flour into an airtight container before storing in the fridge or freezer.