The staff of defense from the Lost Mine of Phandelver Starter Set campaign (p. 53) is a magic staff that grants +1 to AC when attuned. As a magic staff, it also functions as a quarterstaff, which has the versatile property and can be used one-handed.
Can you wield the staff of defense in one hand, and have an actual physical shield equipped in the other hand?
Say I have a Dex score of 16 (a +3 modifier), and the mage armor spell. If I'm also wielding the staff of defense and have a shield equipped, would I have an AC of 13 + 3 + 1 + 2, for a total of 19?