Varied riots occupying left-wingers in Havana in case of importance (8)
I believe the answer is:
Here is my best explanation:
'in havana in case of importance' is the definition.
I can't tell whether this definition defines the answer.
'varied riots occupying left-wingers' is the wordplay.
'varied' indicates an anagram.
'occupying' means one lot of letters goes inside another.
'left wingers' becomes 'hic' (I can't justify this - if you can you should believe this answer much more).
'riots' is an anagram of 'stori'.
'stori' placed inside 'hic' is 'HISTORIC'.
(Other definitions for historic that I've seen before include "Redolent of past glories", "Memorable", "Epoch-making", "Significant", "Of significance in the past", "Important and/or old", "Very important or famous", "Important, from the past", "Pertaining to what is important in the past" and "remarkable".)