Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Procedure; Human Factors
While in climb to FL410 we were given a turn 20 degrees left for traffic.  Passing through 36;600 feet Controller said a mistake had been made and descend to FL360.  As we were descending Controller gave us a right turn to 110. At that time we received an RA which we followed to 35;500 before we were clear of conflict. We then climbed back to FL360 and reported our altitude and RA event to ATC.  ATC stated there was confusion between two controller's plans. The controllers [should be] on the same page. What happened today isn't a surprise to me. Since the reduction in staffing of the controllers from the COVID-19 pandemic flying has been miserable and less safe. Most controllers are controlling several frequencies and are overloaded. We have had more TA's in the last 2 months than the last 3 years.
Corporate jet Captain reported a communication issue between ATC facilities resulted in an airborne conflict.