Disagreeably damp (4)
I believe the answer is:
'disagreeably damp' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for dank that I've seen before include "Clammy, damp" , "Cold and moist" , "Unpleasantly moist" , "Unpleasantly cold and humid" , "Damp, cold, musty" .)