The most common and most likely answer to this crossword clue is the 9 letter word GROUNDING
I've seen this crossword clue in The Daily Telegraph
G
R
O
U
N
D
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G
Buddy explains!

The straight part
We know that "Basic education" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case basic education = grounding.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 GROUNDING mean?
GROUNDING verb- To connect (an electrical conductor or device) to a ground.
- To punish, especially a child or teenager, by forcing him/her to stay at home and/or give up certain privileges.
- To forbid (an aircraft or pilot) to fly.
- To give a basic education in a particular subject; to instruct in elements or first principles.
- To hit a ground ball. Compare fly (verb(regular)) and line (verb).
- To place something on the ground.
- To run aground; to strike the bottom and remain fixed.
- To found; to fix or set, as on a foundation, reason, or principle; to furnish a ground for; to fix firmly.
- To cover with a ground, as a copper plate for etching, or as paper or other materials with a uniform tint as a preparation for ornament.
- To improve or focus the mental or emotional state of.
- Fundamental knowledge or background in a field or discipline.
- The return to a fully conscious state after a psychedelic experience.
- The collision of a ship with ground beneath the surface of the water.
- The prevention of aircraft takeoff because of government action.
- The interconnecting metal chassis/frame of a device, appliance, machine, or metal raceway via a designated conductor to earth at the service panel. It may be bare or covered, and does not carry current in normal operation.
- The absorption of energy through visualized "roots" descending from oneself into the ground, using chi.
- The act by which a child is grounded (forbidden from going out, using electronics, etc.).
- The background of embroidery, etc.