The most common and most likely answer to this crossword clue is the 4 letter word NAZI
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More clues leading to the result NAZI
Buddy explains!

The straight part
We know that "Old fascist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old fascist = nazi.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.
What does NAZI mean?
NAZI noun- A member of the National Socialist German Workers Party (Nationalsozialistische Deutsche Arbeiterpartei, commonly called the NSDAP or Nazi Party).
- One who subscribes to or advocates (neo-)Nazism or a similarly fascist, racist (especially anti-Semitic), xenophobic, ethnic supremacist, or ultranationalist ideology; a neo-Nazi.
- (usually derogatory, sometimes offensive, see usage notes below) One who imposes one’s views on others; one who is considered unfairly oppressive or needlessly strict. (also frequently uncapitalised: nazi)
- A German, a person of German descent, or a person perceived to be of German descent.
- Of or pertaining to the Nazi Party (NSDAP) specifically, or to Nazism, neo-Nazism or neo-Nazis more generally.
- (by extension) Domineering, totalitarian, or intolerant.