Quickness of heartless famous person (8)
I believe the answer is:
celerity
'quickness' is the definition.
(synonyms)
'heartless famous person' is the wordplay.
'heartless' says to hollow out the word (remove centre letters).
'famous person' becomes 'celebrity' (synonyms).
'celebrity' with its centre removed is 'CELERITY'.
'of' is the link.
(Other definitions for celerity that I've seen before include "Rapidity, speediness" , "Expedition" , "Pace" , "Dispatch" , "Haste" .)