Slovenly former nurse drinking coffee extremely languidly (10)
I believe the answer is:
slatternly
'slovenly' is the definition.
('slatternly' can be a synonym of 'slovenly')
'former nurse drinking coffee extremely languidly' is the wordplay.
'former nurse' becomes 'srn' (state registered nurse - former UK nurse title).
'drinking' indicates putting letters inside.
'coffee' becomes 'latte' (I've seen this before**).
'extremely' says to hollow out the word (remove centre letters).
'languidly' with its centre removed is 'ly'.
'srn' enclosing 'latte' is 'slattern'.
'slattern'+'ly'='SLATTERNLY'
(Other definitions for slatternly that I've seen before include "In a sluttish manner" , "Slipshod" , "often in mess" , "(Of a woman) dirty and untidy" , "lacking in tidiness" .)