The most common and most likely answer to this crossword clue is the 9 letter word SPOONFEED
I've seen this crossword clue in The Daily Telegraph
S
P
O
O
N
F
E
E
D
Buddy explains!

The straight part
We know that "Overindulge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case overindulge = spoonfeed.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 SPOONFEED mean?
SPOONFEED verb- To help somebody (usually a baby or elder) to eat using a spoon; to feed using a spoon.
- To overly pamper or indulge someone, so that they do not act or think for themselves.
- To deliver information in as basic a manner as possible.