Wise person, briefly, to sink (3)
I believe the answer is:
sag
'sink' is the definition.
(sagging is a kind of sinking)
'wise person briefly' is the wordplay.
'wise person' becomes 'sage' (I've seen this before).
'briefly' means to remove the last letter.
'sage' with its final letter taken off is 'SAG'.
'to' is the link.
(Other definitions for sag that I've seen before include "Sink, hang down" , "Lose energy" , "Cave in" , "Droop in the middle - it's gas" , "Fail to retain interest" .)