I Left My A-Rank Party anime episode 10, titled "Clover's Back in Action!", marked the Clover Party's re-debut and the beginning of a race into the unnamed dungeon's depths.
While previous episodes stated the mission to be a simple exploration mission, episode 10 marked its evolution into a race between different parties to name this newly formed dungeon. Although the different parties weren't mentioned to be in competition, they did not appear in episode 10.
Disclaimer: This article contains spoilers for I Left My A-Rank Party anime episode 10.
I Left My A-Rank Party anime episode 10 highlights

I Left My A-Rank Party anime episode 10 continued the plot from episode 9 and depicted the Clover Party's journey to the trading capital of Duna. Although the party was on an official mission to explore the newly appeared dungeon, the mission's rather low difficulty and nature had turned the entire situation into another vacation for the Clover Party.
I Left My A-Rank Party anime episode 10 then cut to a montage of the entire Clover Party and their journey to the City of Duna. Upon reaching Duna, Aria inquired about the local cuisines, which resulted in the reveal that Yuke was well-versed in that topic as well. Eventually, Yuke noted the increased number of adventurers in the town while bringing focus to the special attire worn by the Salmutarians.

The robes worn by the Salmutarians were designed to make them stand out while simultaneously revealing their adventuring party and actual status within Salmutarian society. Aria then recommended that the Clover Party also create some special accessories limited to their party.
The episode then cut to Yuke visiting Duna and Silk visiting the Duna Guildmaster, while Aria, Rain, and Nene went to the tavern. The Guildmaster was revealed to be a close associate of Benwood, Yuke's uncle, and one of the few adventurers who had ventured into the deepest parts of the Achromatic Dungeon.

Following the meeting, Yuke and Silk went into the tavern to find their party members, who were being confronted by a few Salmutarian adventurers. Yuke managed to resolve the situation, and the entire party headed for their guild-issued lodging. The next day, the entire party set out for the unnamed dungeon and was briefed on the entire situation.
Adventurer parties from different countries were apparently competing in a race to the dungeon's fifth floor, with the reward being the right to name the dungeon. While the opportunity was enticing, Yuke emphasized that they should just focus on safely reaching the fifth floor, especially since the rest of the competing parties were much more experienced. The episode ended with the Clover Party entering the dungeon.
Final Thoughts
I Left My A-Rank Party anime episode 10 mainly served the purpose of worldbuilding, with the introduction of the Salmutarians alongside the conflict building up due to the unnamed dungeon. Episode 11 will reveal the actual oddities situated within the dungeon.
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