Wife set off in a particular direction (4)
I believe the answer is:
west
'in a particular direction' is the definition.
'wife set off' is the wordplay.
'wife' becomes 'w' (abbreviation).
'off' indicates an anagram.
'set' with letters rearranged gives 'est'.
'w'+'est'='WEST'
(Other definitions for west that I've seen before include "English county" , "Dog (from Argyll?)" , "Mae -, US actress; W" , "The cardinal compass point of 270 degrees" , "One Direction" .)