Vivacity of a ghost (6)
I believe the answer is:
spirit
This clue is a double definition.
'vivacity' is the first definition.
(I've seen this before)
'ghost' is the second definition.
(I've seen this in another clue)
'of a' acts as a link.
(Other definitions for spirit that I've seen before include "Courage; ghost" , "Animating force within living things" , "25 28 [MARS LANDER]" , "Soul - ethos" , "Phantom, ghost" .)