The Staff of Defense is described in the Lost Mine of Phandelver adventure (on p. 53), but the magic items in Appendix A have no rarity mentioned. The Staff of Defense, particularly, is unique to LMoP (i.e. it's not described in the DMG, or any other place I've found). It requires attunement. The description states:
While holding the staff, you have a +1 bonus to your Armor Class.
The staff has 10 charges, which are used to fuel the spells within it. With the staff in hand, you can use your action to cast one of the following spells from the staff if the spell is on your class’s spell list: mage armor (1 charge) or shield (2 charges). No components are required.
The staff regains 1d6 + 4 expended charges each day at dawn. If you expend the staff’s last charge, roll a d20. On a 1, the staff shatters and is destroyed.
What rarity would this item belong to? (This is a question similar to homebrew "what rarity would my homebrew be", but the "homebrew" is actually official.)
This is an useful question for loot distribution.
Best Answer
D&D Beyond lists it as "rare"
The description of the staff of defense on D&D Beyond says:
The description of the staff of defense is only visible on D&D Beyond if you own the Lost Mine of Phandelver adventure there - or at least the item from it. However, you can see its rarity in D&D Beyond's magic item listing even if you don't own the adventure.
This fits with Mike Mearls' (unofficial) statement on Twitter in January 2016: