The most common and most likely answer to this crossword clue is the 8 letter word SIXTIETH
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result SIXTIETH
Buddy explains!

The straight part
We know that "Last one to make third score" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case last one to make third score = sixtieth.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 SIXTIETH mean?
SIXTIETH noun- The person or thing in the sixtieth position.
- One of sixty equal parts of a whole.
- The ordinal form of the number sixty.