You are not expected to warm up and enter the show ring without your coach being present. The in-gate person will generally try to accommodate you in the order, provided you have informed them of the conflict and tried your hardest to get there on time. If you are ready and at the ring, the show management will be more likely to help you out than if you and your horse are absent and not ready to go at a moment's notice.
If the conflict drags on for too long or if you are taking too long to prepare once the conflict has been resolved, the show could institute a time limit for you to enter the ring. In order to avoid this, be organized and plan your day as well as you can!
It's always a good idea to find out which ring has the highest priority of the show. This ring usually has the most important classes, the most classes, or a posted order. Because the show wants this ring to run smoothly, long waits are less likely to be tolerated and trainers should make sure to be on time for that ring.
The lowest priority ring is likely to have longer waits and be more lenient because some trainers must be at the higher priority rings. If you will be showing in a low-priority ring, prepare yourself to wait through conflicts and try not to stress out when it seems as though the conflict will never end. As long as you keep in touch with the in-gate person, the class is not likely to end without you.
Communication is key!