The most common and most likely answer to this crossword clue is the 10 letter word FULL-BLOWN
I've seen this crossword clue in The Times
F
U
L
L
-
B
L
O
W
N
Buddy explains!
The straight part
We know that "at its peak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case at its peak = full-blown.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 FULL-BLOWN mean?
FULL-BLOWN adjective- Completely developed or formed.
- At the peak of blossom; ripe.
- Filled with wind; puffed up.