Piece of vital importance is drooping (4)
I believe the answer is:
limp
'drooping' is the definition.
(I know that drooping can be written as limp)
'piece of vital importance is' is the wordplay.
'piece of' indicates the answer is hidden within the clue.
'LIMP' is hidden in the letters of 'vital importance is'.
(Other definitions for limp that I've seen before include "Flaccid" , "Uneven manner of walking" , "loose" , "Walk with uneven gait" , "Lacking stiffness" .)