Famous person's heartless haste (8)
I believe the answer is:
celerity
'haste' is the definition.
(thesaurus)
'famous person's heartless' is the wordplay.
'famous person' becomes 'celebrity' ('celebrity' can be a synonym of 'famous person').
'heartless' means to remove the middle letters.
'celebrity' with its middle removed is 'CELERITY'.
(Other definitions for celerity that I've seen before include "Dispatch" , "Quickness" , "Swiftness of movement" , "Expedition" , "Pace" .)