The most common and most likely answer to this crossword clue is the 14 letter word WELL-PRESERVED
I've seen this crossword clue in The Times
W
E
L
L
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P
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More clues leading to the result WELL-PRESERVED
Buddy explains!

The straight part
We know that "looking good" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking good = well-preserved.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 WELL-PRESERVED mean?
WELL-PRESERVED adjective- (of an older person) healthy and ageing gracefully
- (of an old, possibly ancient, object) in good condition considering its age.