Measure encountered to the East (4)
I believe the answer is:
mete
'measure' is the definition.
(thesaurus)
'encountered to the east' is the wordplay.
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'to the east' becomes 'e' ('E' can be a synonym of 'east').
'met'+'e'='METE'
(Other definitions for mete that I've seen before include "boundary" , "Dish (out)" , "Dispense, give (out)" , "Apportion" , "To - out is to dispense (eg, justice)" .)