Confesses the snow-drift's getting higher (4,2)
I believe the answer is:
owns up
'confesses' is the definition.
(to own up is to confess)
'snow-drift's getting higher' is the wordplay.
'drift's' indicates anagramming the letters (I've seen 'drifts' mean this).
'getting' says to put letters next to each other.
'higher' becomes 'up'.
'snow' with letters rearranged gives 'owns'.
'owns'+'up'='OWNS UP'
'the' is the link.
(Other definitions for owns up that I've seen before include "Allows" , "'Admits, confesses (4,2)'" , "Admits blame" , "'Comes clean, confesses (4,2)'" , "Confesses, admits guilt" .)