The most common and most likely answer to this crossword clue is the 4 plus 3 letter word SILK HAT
I've seen this crossword clue in The Times
S
I
L
K
H
A
T
More clues leading to the result SILK HAT
Buddy explains!

The straight part
We know that "one coming down on the head at Eton once?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one coming down on the head at eton once? = silk hat.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.