Can something "hold a property"
Solution 1:
Property X holds for the object Y.
This uses hold in the sense "to be valid or true". We can also use "holds true for".
Furthermore, object Y holds some additional properties.
This is using hold in the sense "to have, to possess". So it's valid, but that the same word is used for each is a coincidence.
The latter is a rare use though. I would favour has or maybe exhibits, over holds as more usual.