Mein Assistent wird damit schon klarkommen.

This is translated “My assistant will handle that.” but I’m not sure if this fits with the meaning of the German sentence. My interpretation would be more like “My assistent will come to terms with that.” or “My assistent will be able to manage / get by with that.” I.e. if it were “handle” I would be inclined to use a different German verb, like maybe bearbeiten (which would necessitate changing damit to something else like just es?)

Perhaps if the English sentence were “My assistent will be able to handle that.” then it would be a little better?

I don’t know. Am I misinterpreting the German sentence? The English sentence seems to imply that the assistent is going to directly take care of a specific task that needs to be completed, whereas the German sentence seems to imply that there is some specific constraint that has been placed on the situation, and the assistent will be able work with, under, or around that constraint without any problems.

My dictionary describes klarkommen as informal, so I read the sentence as, ‘My assistant will get it sorted out / cleared up’.

Oh, that’s an interesting case!
In German, we have the anglicism etwas händeln/handlen (I have no idea how it is written since it is strictly reserved for informal, spoken language). It means to manage something despite possible obstacles (and constraints), so basically klarkommen, as you rightfully concluded. The difference between klarkommen and händeln is an added nuance in uncertainty in the former, at least that is how it feels.

Up until now I believed that to handle something does convey a ‘pinch’ of uncertainty as well, basically the same as to manage sth but given your post that might not be true. Possibly, the person who translated the sentence was German as well and thought the same way as I did. Loan words are always tricky.

You’re absolutely right, klarkommen indeed is informal, however I am not sure if sorting out / clearing up aren’t a bit too optimistic. klarkommen implies obstacles and if du mit etwas klargekommen bist, its usually a 80/100 but not perfect. To conclude on that, to me it feels as if @cazort 's proposed ‘My assistent will be able to handle that.’ conveys just enough constraint to get it right.