The most common and most likely answer to this crossword clue is the 2 plus 5 plus 4 letter word AT FIRST HAND
I've seen this crossword clue in The Times
A
T
F
I
R
S
T
H
A
N
D
More clues leading to the result AT FIRST HAND
Buddy explains!

The straight part
We know that "directly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case directly = at first hand.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.