Effectively the team ceases to exist when the changeover (three out, three in) takes place at the end of each season. As the Public Display Clearance is for the nominated pilots as a team, it lapses automatically when the three leave.
And the "old hands" can't forget this - they ALL go back into green flying suits until the next season's clearance is granted. Cyprus does indeed provide guaranteed good weather as well as a handy RAF base to use.
The final clearance is given by the Commander in Chief of Personnel and Training Command (the boss of the non-front line RAF), who also flies with each pilot on the final practices in the run up to new season. Then the clearance is given, break open the fizz (and the red suits!)