Unlike the leagues, you cannot move a competition match from within the bookings diary.
Instead, go to the main Competitions list page by clicking Competitions on the menu.
Click the Manage button on the relevant Competition to reach the main competition page.
This page was used to book the dates to begin with. Now we do a similar action to move a match. Hover the mouse over a booked match (one with a date, time and rink number) and click:
A small window appears with more options:
Click the Book or Move button on the top left to be taken to today's date on the diary:
This view is slightly different to the main diary view. There is a Cancel button on the top, for returning to the competition.
Otherwise, hover over any empty slot to see a Use this slot button:
Using this button will move the match and returns you to the competition main page and the process is complete.