Horses usually act up at the gate when they associate going through the gate with pain or something very unpleasant. If everytime you went past a certain highway sign someone T-boned your car, you'd start to avoid passing the sign, wouldn't you? To change the behavior, you need to reprogram how your horse thinks about the gate.
When your horse became excited at the gate, what was your response? Many riders will automatically take up the tension on their reins because they feel more in control- but if you've got the horse in a curb bit or tom thumb (also a curb) that's painful and will add to the anxiety of the situation.
1. Analyze how you ride the pattern- watch videos if possible. Are you unconsciously using the reins to balance? unintentionally digging a spur in? Asking for speed in a way the horse resents? Any element of the pattern that is unpleasant or painful for your horse can cause them to sour and refuse to enter the arena.
2. You need to work on reassociating the gate with good things. Go to events and jackpots, enter exhibition, and walk the pattern, if you can, show up early and stay late handwalking your horse into the arena or cantering in, halting, dismounting and giving him a treat. Etc. Just mix it up. Show him going through the gate can lead to pleasant things happening.