The most common and most likely answer to this crossword clue is the 5 letter word TALLY
I've seen this crossword clue in The Times
T
A
L
L
Y
More clues leading to the result TALLY
Buddy explains!

The straight part
We know that "score" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case score = tally.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 TALLY mean?
TALLY interjection- Target sighted.
- (by extension) One of two books, sheets of paper, etc., on which corresponding accounts were kept.
- (by extension) Any account or score kept by notches or marks, whether on wood or paper, or in a book, especially one kept in duplicate.
- One thing made to suit another; a match; a mate.
- A notch, mark, or score made on or in a tally; as, to make or earn a score or tally in a game.
- A tally shop.
- A ribbon on a sailor's cap bearing the name of the ship or the (part of) the navy to which they belong.
- A state of cohabitation, living with another individual in an intimate relationship outside of marriage.
- A bone, or piece of wood, on which notches or scores are cut, as the marks of number, for account keeping.
- To count something.
- To record something by making marks.
- To make things correspond or agree with each other.
- To keep score.
- To correspond or agree.
- To check off, as parcels of freight going inboard or outboard.
- In a tall way; stoutly; with spirit.