One German river joining two others? Donner & Blitzen, it might be! (8)

I believe the answer is:

reindeer

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But I can't explain it at all! Could you help me understand?

(Other definitions for reindeer that I've seen before include "D [DECORATION]" , "Dancer, for one" , "Sleigh-puller" , "seasonal transporter" , "Rudolph, for example" .)

I've seen this clue in the Independent.

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