Learjet 55 flight crew reported a pressurization failure during climb necessitated a lower cruising altitude and a return to the departure airport for an overweight landing.

Narrative

I was flying a Lear Jet from ZZZ to ZZZ1; as an FAR Part 91 flight; returning to our home base. The First Officer (FO) was the pilot flying and I was the pilot monitoring. We had flown two previous legs that day and had no issues with the aircraft. On departure the aircraft failed to pressurize. We limited our climb to about 9000 ft. and told ATC that we were dealing with a pressurization issue. I elected to return to ZZZ2 and requested vectors to ZZZ2; rather than ZZZ due to the availability of a longer runways and the potential for better access to appropriate maintenance services. We requested and were vectored for a visual approach to Runway XXL. I requested priority handling since we would be landing over Max Landing Weight. The FO continued to fly the aircraft while I read checklists and communicated with ATC. The approach was uneventful; the touchdown was smooth; and we allowed the aircraft to roll out to taxiway using minimal braking. Taxi to the FBO was uneventful. A post flight visual inspection revealed no obvious anomalies with the landing gear; tires; wheels; or brakes.