Desolate, when left with bill outside (5)
I believe the answer is:
bleak
'desolate' is the definition.
(I know that desolate can be written as bleak)
'left with bill outside' is the wordplay.
'left with' becomes 'l' (common abbreviation. I am not sure about the 'with' bit.).
'bill' becomes 'beak' (synonyms).
'outside' is an insertion indicator.
'l' placed within 'beak' is 'BLEAK'.
'when' acts as a link.
(Other definitions for bleak that I've seen before include "''... House'' (Dickens)" , "raw > fish" , "Gloomy" , "offering little comfort" , "Desolate and barren" .)