The most common and most likely answer to this crossword clue is the 7 letter word GEMINIS
I've seen this crossword clue in The Daily Telegraph
G
E
M
I
N
I
S
More clues leading to the result GEMINIS
Buddy explains!

The straight part
We know that "those delivered in early June?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case those delivered in early june? = geminis.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.