Attend American sanctuary to withdraw (4,1,7)
I believe the answer is:
beat a retreat
'withdraw' is the definition.
(I've seen this before)
'attend american sanctuary' is the wordplay.
'attend' becomes 'be at' (to be at an event is to attend it).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'sanctuary' becomes 're-treat' (retreat can mean a sanctuary or hideout).
'beat'+'a'+'retreat'='BEAT A RETREAT'
'to' is the link.
(Other definitions for beat a retreat that I've seen before include "Go away in a hurry" , "Retire hastily" , "Withdraw quickly" , "Withdraw to avoid something unpleasant" , "Depart hastily" .)