Challenger CL600 First Officer reported experiencing multiple system failures related to air data computer problems. The flight crew was able to resolve the issues and continued to destination.

Narrative

Before the flight the crew picked up the aircraft from the maintenance facility at ZZZ. Work done at the facility included but was not limited to the replacement of the ADC1 computer. There were no issues with the systems of the plane during the taxi and takeoff phases of flight. Approximately 10 minutes into the climb phase of flight the crew lost the Autopilot system; the auto throttle system; airspeed; altimeter; VSI and attitude indicators on the pilot side of the aircraft. Also; the copilot had a loss a flight director on the copilot Primary Flight Display (PFD). While the pilot flew the plane the copilot made a radio call to the ATC facility in use; advising ATC that there was an electrical and Autopilot issue at the time; and vectors and an altitude were needed. No priority handling was requested. The ATC facility gave the flight crew vectors to a hold and to maintain 17;000 ft. Due to the issues with the ADC computer the crew went above the 17;000 feet given to maintain and then descended back down to 17;000. The crew was also advised to hold northwest of the ZZZZZ intersection and were already close to the intersection. The crew attempted to input the correct hold while trying to trouble shoot the ADC issues and did not execute the hold as advised. The issue was then resolved; and the crew request vectors on course to the original flight planned destination.