Possible Clues:

• Animal: German one in three rivers?
• Present-day worker drops precious recording
• One like Rudolph — check red round about tip of nose
• Santa's caribou
• Present drawers?
• Beast runs right round a German river
• Check on what sounds like beloved forest dweller?
• What you might catch from wet pet animal
• Check on reportedly pricey animal
• Animal's about to spill red wine, not whiskey