If you just bought a season pass and completed 100%, It's not just The Syringe that's supposed to appear in your game - Blood Ruby mission, Yak Farm mission, 3 new signature weapons and separate Escape from Durgesh add-on (available from the main menu).
What did and what did not appear in your game?
If this is some activation glitch, you may need to enter your season pass key again in Uplay and try to activate missing content.