Lessen, diminish (7)
I believe the answer is:
dwindle
I believe this clue is a double definition.
'lessen' is the first definition.
(I know that dwindle is a kind of lessen)
'diminish' is the second definition.
(I know that dwindle is a kind of diminish)
(Other definitions for dwindle that I've seen before include "Lessen; fade out" , "'Die down, grow less (7)'" , "Become gradually less or smaller" , "Get smaller, less" , "Grow less and fade away" .)