Left direction to a minimum (5)
I believe the answer is:
least
'a minimum' is the definition.
(I've seen this in another clue)
'left direction' is the wordplay.
'left' becomes 'l' (common abbreviation).
'direction' becomes 'east' (compass direction).
'l'+'east'='LEAST'
'to' is the link.
(Other definitions for least that I've seen before include "To the lowest degree" , "Lowest or smallest" , "Smallest in amount or degree" , "Smallest (in significance)" , "superlatively small" .)