Ask about the task Elvina mentioned

“What is this task you speak of?” You inquire, curious.

"Well, yesterday a warrior bought an enchanted elven rapier from me, and later lost it when he triggered a teleport trap. It is quite a remarkable and expensive weapon and I want it back, but I don't want to waste my time getting it myself. So I want you to get it for me. If you manage to do that... let me think... ah, yes, I think this is a good choice. Wait just a moment!" Elvina moves over to a nearby bookshelf and takes a book. Then she comes back and presents it to you. “I think this will be far more valuable for you than the rapier, don't you agree?”

Even just by looking you can tell that the book is a rare and valuable tome of arcane knowledge. Normally buying it would cost you a small fortune, so getting it for free is VERY tempting.

“I can tell you are interested. Well, if you manage to get the rapier and bring it back to me you get this tome for free, and you also get a discount on all future purchases. Let's say... 25% off. Alternatively, if you manage to get the rapier and then leave the Arena I will come to you and we can trade the rapier for the tome. In that case you get no discount, of course.”

"I don't suppose you know a way to reach the place where the rapier is?" You ask, hopeful.

"Sorry, dear, but due to how the Arena works the exact path changes almost constantly. Trying to give you instructions will not be helpful in the slightest, and might even make things more difficult." Elvina gives you an apologetic look.

"I see... Still, that tome is quite a tempting reward and it won't cost me anything to keep an eye out for the rapier, so I accept the task." You tell the shopkeeper.

"Wonderful!" The older woman gives you a detailed description of the weapon you are supposed to find. "Now then, back to business. Would you like to take a look at my inventory? You never know what might catch your interest..."