Blackmail previously upset communist (6)
I believe the answer is:
extort
'blackmail' is the definition.
(I know that blackmail is a more specific form of the action extort)
'previously upset communist' is the wordplay.
'previously' becomes 'ex' (prefix meaning former or onetime).
'upset' says the letters should be written backwards.
'communist' becomes 'trot' (short for Trotskyist).
'trot' written backwards gives 'tort'.
'ex'+'tort'='EXTORT'
(Other definitions for extort that I've seen before include "Extract money with menaces" , "Obtain money by force or threat" , "Force to fork out" , "Wring (money) out (by violence, etc)" , "Milk" .)