The most common and most likely answer to this crossword clue is the 8 letter word COCKCROW
I've seen this crossword clue in The Guardian
C
O
C
K
C
R
O
W
More clues leading to the result COCKCROW
Buddy explains!
The straight part
We know that "very early in the morning" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very early in the morning = cockcrow.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 COCKCROW mean?
COCKCROW noun- The time of day at which the first crow of a cockerel is heard; dawn or daybreak; first light