The most common and most likely answer to this crossword clue is the 7 plus 5 plus 1 letter word BROUGHT HOME –
I've seen this crossword clue in The Sunday Telegraph
B
R
O
U
G
H
T
H
O
M
E
Â
â
€
“
Buddy explains!
The straight part
We know that "Convincingly made clear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case convincingly made clear = brought home –.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.