Air carrier tractor driver reported during pushback from gate; the tow bar shear pin had sheared. They failed to follow procedures and the aircraft departed without being inspected for damage.

Narrative

I was the lead on Gate XX and I was also the pusher for the aircraft. The push tractor for the Gate is known to have sensitive and touchy brakes. Even when there is the slightest pressure applied to the brakes; the tractor tends to jerk. After the brakes were released and I received the clear to push from the pilot; I started to push. Once I pushed the aircraft far enough and turned him at the appropriate angle to the mark; I started to slowly and gently apply pressure to the brakes; and the tractor had a bad jerking reaction that caused both the aircraft and the tractor to stop abruptly. The pilot asked if everything was OK; to which I responded that the brakes on the tractor were very touchy. I asked for brakes set and the pilot confirmed. My wingwalker disconnect the towbar from the aircraft and after I signaled to disconnect the headset from the aircraft; I noticed that the wingwalker picked up a couple of screws from the ground as I backed the tractor away. When the tractor was parked; my wingwalker brought me the screws and I grew concerned. I checked the towbar and discovered that the sheer pin had broken off. After the next inbound flight which came to the Gate almost right away; I called control from the kiosk phone to ask who to call to replace the sheer pin and I was informed that I was supposed to call over the radio about when the sheer pin broke so maintenance could look at the towbar and the aircraft and I'd have to call a supervisor. I called the zone supervisor to come to the Gate and I explained what happened. This was the first time that a sheer pin broke on me and I wasn't made aware until after the fact; so I didn't know what the procedure was.