The 23-year-old joined up with the squad ahead of this week’s Specsavers County Championship match against Durham at Emirates Riverside.
A product of the Middlesex Academy, Podmore has made eight first-class appearances, returning 25 wickets at an average of 26, including best figures of 4-54 against Somerset.
Director of cricket Kim Barnett, said: “With the return to red-ball cricket, we felt the squad needed another bowling option. Harry comes highly recommended and has performed well in first-class cricket. There is now a lot of competition for places amongst the bowlers.”