Start on satire, finish making lampoon (4,2)
I believe the answer is:
send up
'lampoon' is the definition.
(thesaurus)
'start on satire finish' is the wordplay.
'start on' suggests taking the first letters (I've seen 'starts on' mean this).
'finish' becomes 'endup' ('end up' can be a synonym of 'finish').
The first letter of 'satire' is 's'.
's'+'endup'='SEND-UP'
'making' acts as a link.
(Other definitions for send up that I've seen before include "Parody (of something)" , "skit" , "Despatch aloft to get a humorous imitation" , "Mockery" , "Mock?" .)