The most common and most likely answer to this crossword clue is the 7 letter word MEDIANT
I've seen this crossword clue in Financial Times
M
E
D
I
A
N
T
More clues leading to the result MEDIANT
Buddy explains!

The straight part
We know that "Third" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case third = mediant.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 MEDIANT mean?
MEDIANT noun- The third degree of the diatonic scale.
- A rational number whose numerator is the sum of the numerators of two other given rational numbers and whose denominator is the sum of the denominators of those same two other rational numbers.