A Flight Instructor reported a NMAC with another aircraft in the pattern that was not complying with ATC instructions.

Narrative

My flight student called ZZZ ATC 10 nm northwest of ZZZ with ATIS;requesting the option. ATC directed us to report midfield right downwind for Runway XX. Shortly thereafter; a Cessna called in with ATIS from north of the airport; also requesting the option. ATC directed the Cessna to report entering right base for Runway XX. ATC asked us for a position report; and I believe we reported 5nm northwest. ATC then told us we would be number one for the runway. Then the ATC amended the instructions for the Cessna to enter midfield right downwind for Runway XX. We then reported entering right downwind for Runway XX and ATC cleared us for the option.Before we could respond to the clearance the Cessna responded that he was cleared for the option. At this time my student pilot noticed the ADS-B-in display went red and alerted her to traffic at the same altitude nearby. She deviated south towards the runway and then I looked out and saw the Cessna abeam us; slightly ahead and very close; same altitude; going the same direction. Then I immediately called ATC and reported the Cessna's position. ATC then told us to follow the Cessna and cleared us number 2 for the option. The Cessna landed number one; we landed number two. All ended safely.