Creating Movement Android Game (Touch to move trough gridbased (not diagonals)

Unity Engine
,
1

Well i was looking for some script to attach to my player so when i click over a tile on the gris he automatically walks to.

2

I got this so far

using UnityEngine;

public class TestTouch : MonoBehaviour
{

    private InputManager inputManager;
    private Camera cameraMain;

    // Start is called before the first frame update
    private void Awake()
    {
        inputManager = InputManager.Instance;
        cameraMain = Camera.main;
    }

    private void OnEnable()
    {
        inputManager.OnStartTouch += Move;
    }

    private void OnDisable()
    {
        inputManager.OnEndTouch -= Move;
    }

    public void Move(Vector2 screenPosition, float time)
    {
        Vector3 screenCoordinates = new Vector3(screenPosition.x, screenPosition.y, cameraMain.nearClipPlane);
        Vector3 worldCoordinates = cameraMain.ScreenToWorldPoint(screenCoordinates);
        worldCoordinates.z = 0;
        transform.position = worldCoordinates;
    }
}

But with this code my player only move to the position where i touch like if teletransport.

By the way im new using Unity and learning to program.

Im looking for when i touch it moves smooth until he reach that point touched.

Any help?