What level is your alt's MRD? According to this page, the Brand New Gauntlets are awarded for completing the level 15 Training quest 'Avoid AoE Attacks' - if your MRD is not this level yet, then you can't unlock the quest til then. It makes sense if there is also a main scenario requirement because the level 15 MSQ introduces you to running dungeons for the very first time and, well, some of the first dungeon boss mechanics are AoE attacks.

As always, this game everything is connected to the main scenario (really, the gauntlets are not unique either, there is at least several sets later in the game that also share that model, the Wolfram Gauntlets of Fending being an example, and they're dyeable), so if you're just wanting it for glamour, then it's not really a big deal? Either way, do the main scenario and then try the training regime again and hopefully it should work next time.