Launch unfinished biography with support of aristocrat (4-3)
I believe the answer is:
lift-off
'launch' is the definition.
(I've seen this before)
'unfinished biography with support of aristocrat' is the wordplay.
'unfinished' means to remove the last letter.
'biography' becomes 'life' (synonyms).
'with support of' means one lot of letters go next to another (some letters go beneath or support others).
'aristocrat' becomes 'toff' (toff can mean an upper-class person).
'life' with its final letter taken off is 'lif'.
'lif'+'toff'='LIFT-OFF'
(Other definitions for lift-off that I've seen before include "Launch (of rocket)" , "Start of rocket's journey" , "Moment of rocket's launch" , "Instant when rocket leaves launching pad" .)