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I am going to be graduating in the Spring and have a clerkship lined up for the 2019-2020 cycle. I'd like to apply for DOJ Honors but I'm not sure if I'm out of luck now. I could apply this fall and if I get it start in the Fall of 18 but then I would have to leave DOJ for my clerkship in 2019. Does DOJ allow you to leave for a clerkship and come back after that year is up?

Waiting until I'm at the clerkship to apply isn't really an option because I would no longer be eligible if I work at a firm for the intervening year (though I guess a legal fellowship could cover the gap? But then I'd have to turn down my firm for a fellowship just for a chance to apply for DOJ).

I think you're out of luck, practically if not formally. Even if you'd be allowed to start-leave-return from a conflicts perspective, DOJ isn't going to want to train you to work for a year, then lose you for a year, then spend the resources to re-train you and bring you back up to speed. That said, I'm not an expert on Honors offers (having never seen one), so maybe someone else knows more. In any case, a fellowship or another clerkship would cover you for a year, but you're correct about losing Honors eligibility if you work at a firm. You could also just apply as a lateral hire after your clerkship.