Gradually diminish (7)
I believe the answer is:
dwindle
'gradually diminish' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for dwindle that I've seen before include "Degenerate" , "Shrink, grow smaller" , "Become smaller or fewer" , "Diminish gradually" , "Grow less - waste away" .)