Zack only has access to two accessory slots at the beginning of Crisis Core: Final Fantasy VII Reunion. However, by completing certain missions, you can unlock two additional accessory slots to equip a total of four accessories.
Precious Things Missions
You’ll need to complete two specific missions from the Precious Things section to unlock the two locked accessory slots. The Precious Things missions, or M7-2, are automatically available at the beginning of Chapter 4.
If you already have this mission chain unlocked, work your way to M7-2-2: Search and Destroy II and M7-2-5: Operation: Mako Reactor 3. M7-2-2 automatically unlocks after you clear M7-1-1, and the same process goes for the higher mission numbers.
Once cleared, M7-2-2 rewards the Keychain while M7-2-5 rewards the Backpack. These are the two Key Items you need to unlock the two remaining accessory slots in Crisis Core: Final Fantasy VII Reunion.
The accessory slots will automatically become open once you acquire the aforementioned key items.