Calmly sly about the last appointment (8)
I believe the answer is:
sedately
'calmly' is the definition.
(synonyms)
'sly about the last appointment' is the wordplay.
'about' means one lot of letters goes inside another.
'the last' becomes 'e' (I've seen this in other clues).
'appointment' becomes 'date' (synonyms).
'e'+'date'='edate'
'sly' going around 'edate' is 'SEDATELY'.
(Other definitions for sedately that I've seen before include "Calmly, unhurriedly" , "Primly" , "without getting ruffled" , "With composure" , "Staidly or with dignity" .)