Avoid newspaper offered around hotel (4)
I believe the answer is:
shun
'avoid' is the definition.
(shunning is a kind of avoiding)
'newspaper offered around hotel' is the wordplay.
'newspaper' becomes 'sun' (UK newspaper The Sun).
'offered around' is an insertion indicator.
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'sun' going around 'h' is 'SHUN'.
(Other definitions for shun that I've seen before include "Keep away from Huns" , "Avoid - attention!" , "Spurn; avoid" , "Persistently reject" , "Deliberately avoid" .)