I did the poisoned gladiator quest, it said the Redguard in the fighter quarters had a gift for me, she only gave me the thanks of the other 2 people.

Now I only have a pass to visit the arena fights... How do I actually commit as a gladiator myself?

You don't. There's no gladiator fighting in Morrowind.

I think he is asking help about an arena mod. This is in the wrong section if true.

If not then Pseron is correct. Apart from some of the fights, Arena quarters is largely is for show.