Does spring constantly depend on gravity?

Hint: Let us recall that the earth pulls all the objects towards its center by the force of gravity, which is always acting downwards. So, if we hang an object on the spring vertically downwards then it gets stretched by the gravity acting on the body, and this is stored as the potential energy of the spring.

Complete step by step answer:
According to hooks law, the force which spring will apply or the restoring force developed in the spring is directly proportional to the displacement.
It is given below mathematically.
$ \Rightarrow F = - kx$
Here, $k$ is spring constant and $x$is the displacement in the spring and $F$ is the force Here, a negative sign shows that the force is opposite to the displacement.
From the above formula, we can find the dependency of spring constant as below.
$ \Rightarrow k = \dfrac{F}{x}$
The spring constant only depends on the material used to make the spring and the shape or geometry of the spring. Gravity only affects the net force on the spring and not the spring constant.
Hence, it is independent of gravity. It does not depend on gravity.

Note:
The spring constant remains the same, as hooks law is applicable for all springs.
Suppose an object is attached to the spring vertically. Now measuring this force exerted by the spring on a different planet. The spring will still obey hook’s law here and force will also change on different planets. But this does not mean that the spring constant is variable.
Here, how much the spring is stretched will depend on the weight of the object and the weight in turn depends on gravity. But this will affect the force, not the spring constant. The spring constant will remain the same on different planets having different gravity.