Carriage driver’s optimism about a public disturbance (10)
I believe the answer is:
charioteer
'carriage driver's' is the definition.
'optimism about a public disturbance' is the wordplay.
'optimism' becomes 'cheer'.
'about' means one lot of letters goes inside another.
'public disturbance' becomes 'riot' (I've seen this before).
'a'+'riot'='ariot'
'cheer' going around 'ariot' is 'CHARIOTEER'.
(Other definitions for charioteer that I've seen before include "Ben Hur?" , "Driver common in early warfare" , "Porphyrius perhaps" , "Old carriage driver" , "Driver of Roman vehicle" .)