Cunningly avoid publicity during evening (5)
I believe the answer is:
evade
'cunningly avoid' is the definition.
'evade' can be an answer for 'avoid' (evading is a kind of avoiding). I am not certain of the 'cunningly' bit.
'publicity during evening' is the wordplay.
'publicity' becomes 'ad' (short for advertisement).
'during' is an insertion indicator.
'evening' becomes 'eve' (synonyms).
'ad' going into 'eve' is 'EVADE'.
Can you help me to learn more?
(Other definitions for evade that I've seen before include "Sidestep" , "Dodge, keep clear of" , "Dodge, steer clear of" , "Dodge, duck" , "To get away from" .)