The most common and most likely answer to this crossword clue is the 13 letter word INVESTIGATING
I've seen this crossword clue in The Daily Telegraph
I
N
V
E
S
T
I
G
A
T
I
N
G
Buddy explains!
The straight part
We know that "Looking into" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking into = investigating.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.
What does INVESTIGATING mean?
INVESTIGATING verb- To inquire into or study in order to ascertain facts or information.
- To examine, look into, or scrutinize in order to discover something hidden or secret.
- To conduct an inquiry or examination.