Cogsworth's second friendship quest in Disney Dreamlight Valley, On Her Majesty's Festive Service, unlocks as soon as you hit friendship level four. If you've been spending a lot of time with Cogsworth and completing duties or doing the task you allocated to him at level two, you'll hit this milestone in no time...
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How to complete On Her Majesty's Festive Service in Disney Dreamlight Valley
Source: PC Gamer (opens in a new tab)