Vacuous prince on air – trips up revealing sweat (12)
I believe the answer is:
perspiration
'sweat' is the definition.
(I know that sweat can be written as perspiration)
'vacuous prince on air trips up' is the wordplay.
'vacuous' means to remove the middle letters.
'up' indicates anagramming the letters (letters get chucked up).
'prince' with its middle taken out is 'pe'.
'on'+'air'+'trips'='onairtrips'
'onairtrips' with letters rearranged gives 'rspiration'.
'pe'+'rspiration'='PERSPIRATION'
'revealing' is the link.
(Other definitions for perspiration that I've seen before include "is exuded" , "Sweat" , "Ninety nine percent of genius" .)