The most common and most likely answer to this crossword clue is the 5 plus 3 plus 4 letter word FORTY PER CENT
I've seen this crossword clue in The Times
F
O
R
T
Y
P
E
R
C
E
N
T
Buddy explains!
The straight part
We know that "Score over half a century, say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case score over half a century, say = forty per cent.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.