A Tower Controller in Charge reported the Local Controller cleared an aircraft for takeoff at the same time another aircraft was cleared for a stop and go to an intersecting runway.

Narrative

I was in the stand alone CIC (Controller in Charge) position in the tower with a standard configuration of LC (Local Control) stand alone and FD (Flight Data) /GC/CD (Clarence Delivery) combined. A PRB (Position Relief Briefing) occurred at XA:42 in the LC position. The relieved controller assisted the relieving controller in maneuvering a departure around a point out and a pipeline aircraft before giving their two minute check. There was Aircraft X in the pattern to RWY XX and Aircraft Y taxiing out for departure off RWY XY. A supervisor came up during this time to potential relieve me off the CIC/OS (Operations Supervisor) position. We were discussing if she was going to take the position when a phone came from the Tracon asking her to come down to split the CIC position there. Immediately after the supervisor left the tower cab; LC cleared Aircraft Y for takeoff from RWY XY on runway heading. A few seconds later Aircraft X keyed up and said they were holding on RWY XX. The LC told Aircraft X to continue holding. I asked the LC if I had missed him directing Aircraft X to hold position during the stop portion of the aircrafts stop and go. The LC told me no and that he had forgotten about him. Aircraft Y departed without further incident and Aircraft X continued his pattern work. I watched LC intently until relief was available and then suggested the LC to file a report. I was relieved from CIC a moment or two later and went to the Tracon to discuss the situation with the OS. I allowed myself to be distracted by my discussion with the OS and failed in my oversight duties. I would recommend that when multiple tower certified developmentals are getting proficiency time at once; an operational supervisor is the tower as a stand alone instead of a controller in the CIC role. I would also recommend additional managerial oversight of the controller that was working the LC position.