The most common and most likely answer to this crossword clue is the 6 plus 5 plus 4 plus 5 letter word FIDDLE WHILE ROME BURNS
F
I
D
D
L
E
W
H
I
L
E
R
O
M
E
B
U
R
N
S
Buddy explains!
The straight part
We know that "Get priorities wrong/play as the situation hots up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case get priorities wrong/play as the situation hots up = fiddle while rome burns.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.