I have exceeded maximum indicated speed a few times, every time was as a result of a sudden wind change in excess of 50 kts. The process I had to follow was simple, the event is annotated into the aircraft technical logbook as a defect, and an internal company report is filed as an aircraft limit is exceeded. In an airline environment the company notifies the appropriate authority based upon this report. That is part of the company safety management system.
The aircraft maintenance manual has a procedure for the exceedance, I would send the company an ACARS letting them know it happened so any preparations for the procedure is made prior to landing not to delay the next sector.