A321
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Flight Crew Last 90 Days 240; Flight Crew Total 30000; Flight Crew Type 4000
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Weight And Balance; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Fuel Issue
Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Diverted; General Flight Cancelled / Delayed
Aircraft
Aircraft X - On DATE;  Flight from ZZZ to ZZZ1; made a priority landing due to it being an overweight landing by about 1;500 lbs over max landing weight and a fuel system Fault problem. Landing at ZZZ2.Fuel system Fault caused by the Left Aft Aux tank failed to transfer to center tank.  Preformed ECAM procedure; called company Dispatch and Company Maintenance to help trouble shoot; but was unable to get fuel out of Aux tank. Myself; my First Officer; Dispatch and Maintenance all agreed best action was to land at ZZZ2; overweight if needed; to get repairs and for better care of passengers.Priority handling was requested with ATC; which is called for in our Company Manual (QRH). CFR was standing  at ZZZ2 on landing. Urgency was due to overweight landing and fuel system problem.
A321 Captain reported a fuel transfer problem caused a diversion and precautionary landing.