Parody about head of state becomes successful (5,3)
I believe the answer is:
takes off
'becomes successful' is the definition.
(I've seen this in another clue)
'parody about head of state' is the wordplay.
'parody' becomes 'takeoff' (synonyms).
'about' indicates putting letters inside.
'head of' indicates taking the first letters.
The first letter of 'state' is 's'.
'takeoff' enclosing 's' is 'TAKES OFF'.
(Other definitions for takes off that I've seen before include "becomes popular" , "Does a strip" .)