Announced imported cheeses move briskly (6)
I believe the answer is:
breeze
'move briskly' is the definition.
'breeze' can be an answer for 'move' (breezing is a kind of moving). I am unsure of the 'briskly' bit.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for breeze that I've seen before include "breath of fresh air" , "Something very easy to do (colloq.)" , "is this enough to blow out candles?" , "Slight wind" , "Given piece of cake" .)