Slovenly old nurse left Derby at last, drinking coffee (10)
I believe the answer is:
slatternly
'slovenly' is the definition.
(synonyms)
'old nurse left derby at last drinking coffee' is the wordplay.
'old nurse' becomes 'SRN' (abbreviation of state registered nurse).
'left' becomes 'l' (common abbreviation).
'at last' says to take the final letters.
'drinking' indicates putting letters inside (inserted letters are consumed or drunk).
'coffee' becomes 'latte' (type of coffee drink).
The last letter of 'derby' is 'y'.
'srn'+'l'+'y'='srnly'
'srnly' going around 'latte' is 'SLATTERNLY'.
(Other definitions for slatternly that I've seen before include "In a sluttish manner" , "often in mess" , "lacking in tidiness" , "(Of a woman) dirty and untidy" , "Slipshod" .)