Untrue story I tell is curtailed, interrupted by sign of drunkenness (8)
I believe the answer is:
mythical
'untrue' is the definition.
(thesaurus)
'story i tell is curtailed interrupted by sign of drunkenness' is the wordplay.
'story i tell' becomes 'my tale'.
'is curtailed' means to remove the last letter.
'interrupted by' means one lot of letters goes inside another.
'sign of drunkenness' becomes 'hic'.
'mytale' with its last letter removed is 'mytal'.
'mytal' placed around 'hic' is 'MYTHICAL'.
(Other definitions for mythical that I've seen before include "Imaginary or based on folk tales" , "Fabulous; fictitious" , "Based on fable" , "Legendary" , "Existing in legends or traditional stories" .)