The next arena after Wendy joins is in Chapter 11 (on Echidna's route only). As Panthera observes, sending Wendy into the arena is risky, so I recommend that anyone who wishes to do so support abuse first. FE6's arena does not take away support bonuses, and entering an "even fight" with something like +3 Atk, +15 Hit and +7 Avoid from A Bors alone can make a world of difference.
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I don't like this duchy. Now, it's an adventurer.