The most common and most likely answer to this crossword clue is the 9 letter word RECHERCHÉ
I've seen this crossword clue in Independent
R
E
C
H
E
R
C
H
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More clues leading to the result RECHERCHÉ
- European blocking repeat of republican revolutionary’s choice
- Far-fetched about revolutionary repeatedly throttling King
- Choice role void — US entertainer almost beside herself!
- Peculiar revolutionary repeatedly claimed right to follow religious education
- Obscure singer about to enter here, dancing
- Exquisite woman in a kind of crèche
- Carefully chosen soldiers meeting revolutionary beginning to recognise him
- Frenzied cheer about a pop singer is rare
- Exotic day-care centre’s leader off to welcome singer
- Little known about revolutionaries seizing queen
Buddy explains!

The straight part
We know that "Obscure" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obscure = recherchÉ.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 RECHERCHÉ mean?
RECHERCHÉ adjective- Exquisite; lavishly elegant and refined.
- Exotic or obscure.