Awfully dry outlaw, on the surface (9)
I believe the answer is:
outwardly
'on the surface' is the definition.
(I've seen this in another clue)
'awfully dry outlaw' is the wordplay.
'awfully' indicates an anagram.
'dry'+'outlaw'='dryoutlaw'
'dryoutlaw' with letters rearranged gives 'OUTWARDLY'.
(Other definitions for outwardly that I've seen before include "On the face of it" , "As far as appearances are concerned" , "Superficially" , "Externally" .)