The most common and most likely answer to this crossword clue is the 5 plus 4 plus 2 plus 3 letter word OTHER FISH TO FRY
I've seen this crossword clue in The Times
O
T
H
E
R
F
I
S
H
T
O
F
R
Y
More clues leading to the result OTHER FISH TO FRY
Buddy explains!
The straight part
We know that "higher priorities" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case higher priorities = other fish to fry.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.