The most common and most likely answer to this crossword clue is the 8 letter word TUTORING
I've seen this crossword clue in The Guardian
T
U
T
O
R
I
N
G
More clues leading to the result TUTORING
Buddy explains!

The straight part
We know that "Instruction" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case instruction = tutoring.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 TUTORING mean?
TUTORING verb- To instruct or teach, especially an individual or small group.
- To treat with authority or sternness.
- Tuition