The most common and most likely answer to this crossword clue is the 9 plus 6 letter word STARTER’S ORDERS
I've seen this crossword clue in The Guardian
S
T
A
R
T
E
R
â
€
™
S
O
R
D
E
R
S
Buddy explains!
The straight part
We know that "First course requests/under which they’ll soon be off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first course requests/under which they’ll soon be off = starter’s orders.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.