Примерно так должно работать.
using UnityEngine;
using UnityEngine.UI;
public class ClickExample: MonoBehaviour
{
public Button moveUpButton;
public Button moveDownButton;
[Space]
public GameObject target;
void OnEnable()
{
moveUpButton.onClick.AddListener(MoveUp);
moveDownButton.onClick.AddListener(MoveDown);
}
void MoveUp()
{
target.transform.position += new Vector3(0f, 1f, 0f);
}
void MoveDown()
{
target.transform.position -= new Vector3(0f, 1f, 0f);
}
}