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

The straight part
We know that "fully alert" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fully alert = wide-awake.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 WIDE-AWAKE mean?
WIDE-AWAKE adjective- Completely or fully awake
- Alert, vigilant or watchful
- A bird, the sooty tern.
- A type of hat with a broad brim made of black or brown felt.