Date: 202108
Local time of day: 1201-1800
Location: ZZZ2.TRACON, US
Flight conditions: VMC
Light: Daylight
Aircraft: Falcon 900
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Aircraft component: Hydraulic System Pump
Component problem: Malfunctioning
Reporter organization: Corporate
Reporter function: First Officer; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Troubleshooting; Time Pressure
Second reporter function: Pilot Not Flying; Captain
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Separated Traffic; Flight Crew Overcame Equipment Problem; Flight Crew Landed As Precaution; Flight Crew Requested ATC Assistance / Clarification; General Maintenance Action
Contributing factors: Human Factors; Aircraft; Procedure
Primary problem: Aircraft

Narrative: Midway through the flight from ZZZ to ZZZ1 we received 'HYDR #1 PUMP 3' CAS (Crew Alert System) message. The QRH states that system operating times will take longer than expected and that no other action was required. We continued the flight after notifying home base of the situation. Quantity showed 100% on the synoptic page with a pressure stabilized at 3;000 psi.On the arrival to ZZZ1 we were given a level off altitude and 'HYDR #1 PUMP 1' CAS message appeared. Soon after pressure fluctuated between 0 and 3;000 psi. causing CAS messages to appear then extinguish when pressure was high. Due to sequencing into ZZZ1 we had extended vectors for the ILS XX circle to land runway YY. During this time The PIC and I decided we would configure early so I could get a feel of the aircraft and allow extra time for gear extension; flap extension; ect. After being established on a long final for runway XX circle YY; I asked for gear down. We received 3 red down arrows but heard what I would consider normal gear down. We then overflew the airfield so tower could view if the gear was down then executed the missed approach for the ILS XX.The tower reported the gear was down but our indication was three red arrows. After being handed off to ZZZ2 we received delay vectors to trouble shoot the gear issue. At this time hydraulic quantity on system 1 was zero. Because we had a red gear indication; PNF followed the checklist that included pulling the gear T-handle. We still had three red gear indications so we followed the checklist for the gravity free fall. Because the checklist required 190 knots for gravity gear drop I commanded the aircraft to clean wing. This set off additional 'inboard slat fail' CAS message and we added the landing distance penalty required by the checklist.The PNF then followed the checklist for the gravity gear deploy checklist. He pulled the left main gear pull-handle and I applied full left rudder per the checklist; resulting with a left main gear down green indication. As I returned the aircraft to rudder neutral the nose gear indicated down and locked. The PNF then pulled the right main gear pull handle and after applying a slight right rudder the right main gear appeared down and locked. The PNF finished the checklist and we had a three green gear indication.We determined because of the hydraulic/gear issues it was in our best interest to declare an emergency and return to ZZZ and have crews standing by in the event the gear would collapse. Airport conditions were VFR and favored runway XX. We landed the airplane as a non-event and were towed to the FBO due to the loss of nose wheel steering.


Second narrative: [Narrative contained no additional information.]


Synopsis: Flight crew reported a hydraulic pump failure in flight and requested priority handling to make a precautionary landing at destination airport.