The most common and most likely answer to this crossword clue is the 5 letter word ULTRA
I've seen this crossword clue in Financial Times
U
L
T
R
A
More clues leading to the result ULTRA
- Extremist cult rarely demonstrates
- Extremist involved in awful tragedy
- Immoderate posh officer joins gunners
- Extremist in bizarre rituals is thrown out
- Extremist's last month, with troops in pursuit
- Extreme overhaul transforms houses
- Diehard gunmen support superior officer
- Fanatic given such sound treatment?
- You sell feminist underwear, bottoms only, leading to end of bra? That’s radical
- Extreme offering from Hoggart luckily withdrawn
Buddy explains!

The straight part
We know that "Extremist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extremist = ultra.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 ULTRA mean?
ULTRA noun- An ultraroyalist in France.
- An extremist, especially an ultranationalist.
- An especially devoted football fan, typically associated with the intimidating use of extremist slogans, pyrotechnics and sometimes hooligan violence.
- An ultramarathon.
- An ultra-prominent peak.
- (usually capitalised) Code name used by British codebreakers during World War 2 for decrypted information gained from the enemy.
- Extreme; far beyond the norm; fanatical; uncompromising.