Escape notice coming in the day before (5)
I believe the answer is:
'escape' is the definition.
(evading is a kind of escaping)
'notice coming in the day before' is the wordplay.
'notice' becomes 'ad'.
'coming in' means one lot of letters goes inside another.
'the day before' becomes 'eve' (I've seen this before).
'ad' inserted within 'eve' is 'EVADE'.
(Other definitions for evade that I've seen before include "Dodge by cleverness or trickery" , "Escape, avoid" , "Illegally escape (taxes)" , "Slyly escape" , "Dodge, steer clear of" .)