Go by the east: a mistake (6)
I believe the answer is:
elapse
'go by' is the definition.
('elapse' can be a synonym of 'go by')
'the east a mistake' is the wordplay.
'the east' becomes 'e' ('E' can be a synonym of 'east').
'a mistake' becomes 'lapse' (lapse is a kind of mistake).
'e'+'lapse'='ELAPSE'
(Other definitions for elapse that I've seen before include "Go by - pass away" , "Please (anag) -- pass away" , "Glide by" , "'Pass by, as time (6)'" , "Pass away - asleep (anag)" .)