Examination, as soon as it's finished (4-4)
I believe the answer is:
once-over
'examination' is the definition.
(I know that once-over is a type of examination)
'as soon as it's finished' is the wordplay.
'as soon as' becomes 'once' (once can mean immediately after).
'it's finished' becomes 'over' (over can mean finished or ended).
'once'+'over'='ONCE-OVER'
(Other definitions for once-over that I've seen before include "Cursory examination" , "Appraising glance" , "Brief check" , "Quick appraisal" , "Quick inspection" .)