Wrongdoing outside public house by inscrutable person (6)
I believe the answer is:
sphinx
'inscrutable person' is the definition.
(I know this)
'wrongdoing outside public house by' is the wordplay.
'wrongdoing' becomes 'sin' (sin is a kind of wrongdoing).
'outside' is an insertion indicator.
'public house' becomes 'ph' (abbreviation).
'by' becomes 'x' (as in 'multiplied by').
'sin' going around 'ph' is 'sphin'.
'sphin'+'x'='SPHINX'
(Other definitions for sphinx that I've seen before include "Riddling monster of myth" , "Riddling monster, top half a woman, bottom half a lion" , "Egyptian statue with lion's body and human head" , "Riddling monster of Greek mythology" , "Egyptian stone statue - inscrutable person" .)