The most common and most likely answer to this crossword clue is the 10 letter word MILLENNIAL
I've seen this crossword clue in The Times
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More clues leading to the result MILLENNIAL
Buddy explains!

The straight part
We know that "for a very long time" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case for a very long time = millennial.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 MILLENNIAL mean?
MILLENNIAL noun- A demographic term for a person from the generation born from around the early 1980s to the mid 1990s or early 2000s; individuals who reached adulthood early in the 3rd millennium, C.E.
- Referring to the 1,000th anniversary of an event or happening.
- Occurring every thousand years.
- Occurring at the end or beginning of a millennium.
- Of or relating to people born in the last two decades of the 20th century.
- Referring to the millennium, the period of one thousand years during which Christ will reign on earth.