LR-60 First Officer reported an autoflight malfunction during the climb on a test flight. The aircraft returned to the departure airport; and landed.

Narrative

I served as the First Officer on board for a test flight out of ZZZ. The flight was conducted with two pilots on board and had a filed route of ZZZ to ZZZ; with 'test flight' appropriately noted in the ATC remarks.The purpose of the flight was to evaluate the aircraft following recent maintenance; specifically addressing known autopilot issues. Upon departure; the aircraft rotated normally and became airborne without any immediate concerns. Shortly after takeoff; however; the captain lost his flight director and multiple error flags displayed on the PFD (Primary Flight Display). A positive exchange of controls was conducted; and I assumed control of the aircraft. We continued the test flight as planned.During the climb and initial maneuvering; we experienced a loss of both the transponder and TCAS systems. ATC promptly identified the loss of our transponder signal and issued vectors for us to return to the airport. Despite the failure; ATC was still able to monitor our position on their radar.As we were being vectored; ATC advised us to fly a heading of either 080 or 090 degrees (the exact heading is unclear in hindsight). All of our onboard navigation displays and instrumentation indicated that we were flying the commanded heading. However; ATC informed us that we were approximately 40 degrees off the assigned course.Upon receiving this information; we immediately corrected the deviation. During the turn; we regained visual contact with the airport and proceeded with a visual approach for a safe and uneventful landing at ZZZ.All checklists and communication protocols were followed appropriately. We coordinated closely with ATC throughout the event and prioritized safety and situational awareness during the return.