The most common and most likely answer to this crossword clue is the 7 plus 6 letter word OPENING SPEECH
O
P
E
N
I
N
G
S
P
E
E
C
H
Buddy explains!
The straight part
We know that "First delivery/address number one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first delivery/address number one = opening speech.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.