The most common and most likely answer to this crossword clue is the 7 letter word TERNARY
I've seen this crossword clue in The Daily Telegraph
T
E
R
N
A
R
Y
Buddy explains!

The straight part
We know that "based on three" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case based on three = ternary.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 TERNARY mean?
TERNARY noun- A group of three things; a trio, threesome or tierce.
- The Holy Trinity.
- Made up of three things; treble, triadic, triple, triplex.
- Arranged in groups of three.
- To the base three.
- Having three variables.
- Containing, or consisting of, three different parts, as elements, atoms, groups, or radicals, which are regarded as having different functions or relations in the molecule.