Droops; county (5)
I believe the answer is:
wilts
This clue is a double definition.
'droops' is the first definition.
(I know this)
'county' is the second definition.
(short for Wiltshire)
(Other definitions for wilts that I've seen before include "(Of foliage) goes limp" , "Southern county" , "part of the kingdom" , "Flags" , "A county (abbr.); suffers from 1" .)