The post is attached to concrete using Simpson Tie 4x4 post tie. The top of post flexes a good 2-3 inches when gate shuts against it. How can I stabilize it?
There are many variants of Simpson Strong Tie post supports. Most bolt into the concrete pad or have legs embedded into the fresh poured concrete. The post is nailed or bolted to the tie. The compliance is likely at that joint, and you can up-size the through bolts to tighten things up. If the compliance is actually at the pad to Tie, the fix is more involved as it could involve getting into the concrete. Can you provide pics of your specific Simpson Strong Tie configuration to assist?