The most common and most likely answer to this crossword clue is the 5 letter word LENIN
I've seen this crossword clue in The Times
L
E
N
I
N
More clues leading to the result LENIN
- Noted traveller in train to Petrograd, returning 9.50?
- Somewhat Phoenixlike this old leader, were he to rise?
- Revolutionary number left heading west
- Revolutionary man of the cloth, one swapping with European
- Old communist, revolutionary figure on left
- Number fifty in uprising, communist
- Revolutionary leader initially followed by figure from east
- Famous Red Square building's fourth from the right
- Old red sheets one earl switched around
- Revolutionary heading from Leicester Square returns
Buddy explains!

The straight part
We know that "communist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case communist = lenin.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.