Persuaded to leave a tumbledown shack (3)
I believe the answer is:
led
'persuaded' is the definition.
(I've seen this in another clue)
'leave a tumbledown shack' is the wordplay.
'leave' indicates a hidden word (I've seen 'leaving' mean this (the answer must leave the confines of the clue)).
'LED' can be found hidden inside 'tumbledown shack'.
'to' is the link.
(Other definitions for led that I've seen before include "Paved the way" , "showed the way ahead" , "was in the van" , "Light-emitting diode (abbr.)" , "sort of light" .)