Rather drunk in outrageous tale (1,6)
I believe the answer is:
a little
'rather' is the definition.
(I've seen this before)
'drunk in outrageous tale' is the wordplay.
'drunk' becomes 'lit' (I've seen this in other clues).
'in' means one lot of letters goes inside another.
'outrageous' indicates anagramming the letters (I've seen this in other clues).
'tale' with letters rearranged gives 'atle'.
'lit' inserted inside 'atle' is 'A LITTLE'.
(Other definitions for a little that I've seen before include "to some degree" , "Rather" .)