As somebody who was labelled as gifted from a young age, I have some advice from a different angle.
I caused a lot of problems at school, right from nursery.
Do not let people keep telling your son how smart he is. Tell the teachers not to single him out for praise. Treat him the same as every other child. Doing so will encourage him to try harder to stand out in a positive way.
He likes the praise, who doesn't? But he doesn't like the teasing that no adult ever sees or hears. Children don't like to be called geeks, not early on anyway. Also, you may inadvertently give him a superiority complex, or may have done so already, which isn't healthy for anyone.
I read something somewhere, that said you should not keep telling a child they are very smart, but instead give them praise only when they complete a task. It made a lot of sense to me, and I had a teacher who would do that for me, and she was my favourite.
More likely than anything he doesn't want to stand out, he wants to fit in. Children tease each other when they're jealous of the praise that one receives.
Challenge him with difficult tasks, designed for children above his age. When he completes them, do not do backflips, just say "well done" and move on.
Find him a mentor, or someone to look up to. More often than not, it will not be you that he looks up to. Additionally, it could really help for him to meet a child similar to himself, to work with them and be competitive. Together they can push each other, and whilst they're concentrating on difficult work, he won't have time to focus on being disruptive or trying to look cool.
For the love of God, do not place huge expectations on his shoulders, do not keep saying "you could achieve great things", treat him like a normal child.
Finally, maybe not yet, but in future, talk to him like an adult, but treat him like a child. He will understand.
Do not put him on a pedestal, if you do you're only setting him up for long fall if he makes mistakes. Challenge him.
This could have been written far better, but I'm not a psychologist, I'm merely offering advice on what did or could've worked for me.