The most common and most likely answer to this crossword clue is the 3 plus 4 plus 3 letter word BIT ONES LIP
I've seen this crossword clue in Financial Times
B
I
T
O
N
E
S
L
I
P
Buddy explains!
The straight part
We know that "Buttoned up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case buttoned up = bit ones lip.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.