Maybe arrive at the place you're showing at way ahead of time (if you can), and just groom your horse there, or do things he enjoys. This will hopefully help him relax and be comfortable in his surroundings. Also, just try and walk him around the area until he relaxes walking about xx
There are legal oral calmers available now, though you should always double check the shows rules and list of prohibited substances. After that maybe try stick to a familiar warm up routine, try pick a quiet area to warm up and take him out in plenty of time. You could try training shows to get him used to shows without the pressure
Maybe lunge I forgot you have time. Do exercises that are familiar to him such as figure 8s or leg yields or lots of transitions. Maybe try a calming additive that's non swabbable in his feed such as Hush or Mag E? Also make sure you're not nervous and gripping with your legs without knowing. Also before you go in the arena, take a deep breath, both feet out of the stirrup so and just sit there so you horse can relax, then slowly put your feet in your stirrups and collect your reigns.