The most common and most likely answer to this crossword clue is the 5 plus 4 plus 5 plus 6 letter word FIRST COME FIRST SERVED
I've seen this crossword clue in The Times
F
I
R
S
T
C
O
M
E
F
I
R
S
T
S
E
R
V
E
D
Buddy explains!
The straight part
We know that "as queue dealt with?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case as queue dealt with? = first come first served.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.