The most common and most likely answer to this crossword clue is the 7 letter word ARCHAIC
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More clues leading to the result ARCHAIC
- Out of date leading article I initially cut
- Old-fashioned tea served in a racing club
- Ancient New Testament language church introduced, not in the morning
- Very old chief meets foreign agents from the east
- Old broken chair engulfed by current
- Antique piece of furniture without Mr Chippendale’s initial
- Antique Art Chair Co Ltd
- Cunning answer, I see, is out of date
- Old investigators return and follow crook?
- Old-fashioned roguish spies turned up
Buddy explains!

The straight part
We know that "Obsolete" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obsolete = archaic.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 ARCHAIC mean?
ARCHAIC noun- (usually capitalized) A general term for the prehistoric period intermediate between the earliest period (‘Paleo-Indian’, ‘Paleo-American’, ‘American‐paleolithic’, &c.) of human presence in the Western Hemisphere, and the most recent prehistoric period (‘Woodland’, etc.).
- (paleoanthropology) (A member of) an archaic variety of Homo sapiens.
- Of or characterized by antiquity; old-fashioned, quaint, antiquated.
- (of words) No longer in ordinary use, though still used occasionally to give a sense of antiquity.
- Belonging to the archaic period