First of all please note I have never been banned on anything, but I have a plan if I was.
You can probably guess why I made this.
So here are the steps.
1) Make sure you do nothing with TPT for a week.
2) Make an account with a name not reflecting your old account. Change your avatar.
3) Straight after the new account is ready start posting fresh
4) Make sure people know your old account, and you want to start again.
6) Use 100% correct grammar.
7) Wait to see what people think. If people flame, stay calm.
Not to do:
Spam the forum with endless accounts. Say you should not have been banned. Blame it all on someone. Act as if your not your old banned account. Not admit to your mistakes. Plead for your old account back. Say 'Why?!' too many times. Don't hate @Simon . He is our God!
I hope this shows what you should do if banned and want to keep playing TPT.
Making a new thread with your new account is spam, unnecessary, and just pointless. No one cares if you've decided to not do whatever got you banned in the first place.