Secret: keep away from publican (5)
I believe the answer is:
inner
'secret' is the definition.
(I've seen this before)
'keep away from publican' is the wordplay.
'away from' indicates named letters should be taken away.
'publican' becomes 'innkeeper' (a publican runs a pub).
'innkeeper' with 'keep' taken away is 'INNER'.
(Other definitions for inner that I've seen before include "Relating to the soul, mind or spirit" , "Opposite of 13" , "Area near to bull's-eye" , "Part of an archery target" , "Located or occurring closer to a centre" .)