The most common and most likely answer to this crossword clue is the 4 plus 1 plus 6 letter word BLOW A GASKET
B
L
O
W
A
G
A
S
K
E
T
Buddy explains!
The straight part
We know that "Lose temper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lose temper = blow a gasket.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.