goDragMeスクリプトをAddComponentしてください。イベントハンドラを利用してUIのImageをドラッグ＆ドロップします。m_OnEventPointerBegin、m_OnEventPointerEndにはドラッグ開始/終了時のコールバック関数が登録できます。

using UnityEngine;
using UnityEngine.EventSystems;
using UnityEngine.UI;
 
//-------------------------------------------------------------
//! ドラッグ＆ドロップ規定クラス
//-------------------------------------------------------------
public class goDragMeBase : MonoBehaviour
{
    public delegate void CallbackFuncPointer( PointerEventData _eventData );
    public CallbackFuncPointer m_OnEventPointerBegin;
    public CallbackFuncPointer m_OnEventPointerEnd;
 
    protected Canvas m_canvas;
    protected bool m_dragOnSurfaces = true;
    protected GameObject m_draggingIcon = null;
    protected RectTransform m_draggingPlane = null;
 
    //-------------------------------------------------------------
    //! ドラッグ処理中か？
    //-------------------------------------------------------------
    public bool IsDragging()
    {
        return (m_draggingIcon != null) ? true : false;
    }
 
    //-------------------------------------------------------------
    //! 親を探す。
    //-------------------------------------------------------------
    protected T FindInParents<T>(GameObject _go) where T : Component
    {
        if (_go == null)
        {
            return null;
        }
        var comp = _go.GetComponent<T>();
 
        if (comp != null)
        {
            return comp;
        }
 
        Transform t = _go.transform.parent;
        while (t != null && comp == null)
        {
            comp = t.gameObject.GetComponent<T>();
            t = t.parent;
        }
        return comp;
    }
 
    //-------------------------------------------------------------
    //! イメージ作成
    //-------------------------------------------------------------
    protected Image createImage(Canvas _canvas, PointerEventData _eventData)
    {
        m_canvas = _canvas;
 
        // GameObjectの作成。
        m_draggingIcon = new GameObject(_eventData.selectedObject.name);
 
        // 親子関係設定
        m_draggingIcon.transform.SetParent(_canvas.transform, false);
 
        // 最前面に表示する。
        m_draggingIcon.transform.SetAsLastSibling();
 
        // イメージ追加
        Image image = m_draggingIcon.AddComponent<Image>();
 
        // 当たり無効。
        m_draggingIcon.AddComponent<IgnoreRaycast>();
 
        // スプライト設定。
        image.sprite = gameObject.GetComponent<Image>().sprite;
        image.SetNativeSize();
 
        return image;
    }
 
    //-------------------------------------------------------------
    //! 座標更新
    //-------------------------------------------------------------
    protected void SetDraggedPosition(PointerEventData _eventData)
    {
        if (m_dragOnSurfaces && _eventData.pointerEnter != null && _eventData.pointerEnter.transform as RectTransform != null)
        {
            m_draggingPlane = _eventData.pointerEnter.transform as RectTransform;
        }
 
        RectTransform rt = m_draggingIcon.GetComponent<RectTransform>();
        Vector3 globalMousePos;
        if (RectTransformUtility.ScreenPointToWorldPointInRectangle(m_draggingPlane,
            _eventData.position, _eventData.pressEventCamera, out globalMousePos))
        {
            rt.position = globalMousePos;
            rt.rotation = m_draggingPlane.rotation;
        }
    }
}
 
//-------------------------------------------------------------
//! ドラッグ＆ドロップ
//-------------------------------------------------------------
public class goDragMe : goDragMeBase, IBeginDragHandler, IDragHandler, IEndDragHandler
{
    //-------------------------------------------------------------
    //! ドラッグ開始
    //-------------------------------------------------------------
    public void OnBeginDrag(PointerEventData _eventData)
    {
        var canvas = FindInParents<Canvas>(gameObject);
        if (canvas == null)
        {
            return;
        }
 
        Image image = createImage(canvas, _eventData);
        if (image != null)
        {
            if (m_dragOnSurfaces)
            {
                m_draggingPlane = transform as RectTransform;
            }
            else
            {
                m_draggingPlane = canvas.transform as RectTransform;
            }
 
            SetDraggedPosition(_eventData);
        }
 
        if (m_OnEventPointerBegin != null)
        {
            m_OnEventPointerBegin(_eventData);
        }
    }
 
    //-------------------------------------------------------------
    //! ドラッグ中
    //-------------------------------------------------------------
    public void OnDrag(PointerEventData _eventData)
    {
        if (m_draggingIcon != null)
        {
            SetDraggedPosition(_eventData);
        }
    }
 
    //-------------------------------------------------------------
    //! ドラッグ終了
    //-------------------------------------------------------------
    public void OnEndDrag(PointerEventData _eventData)
    {
        if (m_OnEventPointerEnd != null)
        {
            m_OnEventPointerEnd(_eventData);
        }
 
        if (m_draggingIcon != null)
        {
            Destroy(m_draggingIcon);
            m_draggingIcon = null;
        }
    }
}

goDragMeForLongPress スクリプトをUIにAddComponenntしてください。こちらはドラッグ開始のきっかけが触れた時ではなく長押し時に変更したものになります。

//-------------------------------------------------------------
//! 長押しからのドラッグ＆ドロップ
//-------------------------------------------------------------
public class goDragMeForLongPress : goDragMeBase,
IDragHandler, IEndDragHandler,
IPointerDownHandler, IPointerUpHandler, IPointerExitHandler
{
private float m_longPressTime = 0.16f;
private float m_timer = 0.0f;
private bool m_isPress = false;
private PointerEventData m_eventData = null;
 
//-------------------------------------------------------------
//! 長押し判定時間の設定。
//-------------------------------------------------------------
public void SetLongPressTime(float _time)
{
    m_longPressTime = _time;
}
 
//-------------------------------------------------------------
//! 状態のクリア。
//-------------------------------------------------------------
private void clearStatus()
{
    m_isPress = false;
    m_timer = 0.0f;
    m_eventData = null;
}
 
public void OnPointerDown(PointerEventData _eventData)
{
    m_isPress = true;
    m_timer = 0.0f;
    m_eventData = _eventData;
 
    if (m_OnEventPointerBegin != null)
    {
        m_OnEventPointerBegin(m_eventData);
    }
}
 
public void OnPointerUp(PointerEventData _eventData)
{
    // ドラッグせずに指を離した。
    GameObject go = _eventData.pointerCurrentRaycast.gameObject;
    if (_eventData.selectedObject == go)
    {
        if (m_OnEventPointerEnd != null)
        {
            m_OnEventPointerEnd(_eventData);
        }
 
        if (m_draggingIcon != null)
        {
            Destroy(m_draggingIcon);
            m_draggingIcon = null;
        }
        clearStatus();
    }
}
 
public void OnPointerExit(PointerEventData _eventData)
{
    clearStatus();
}
 
public void Update()
{
    if (m_isPress)
    {
        m_timer += Time.deltaTime;
 
        if (m_timer >= m_longPressTime)
        {
            // ドラッグ開始。
            var canvas = FindInParents<Canvas>(gameObject);
            if (canvas == null)
            {
                return;
            }
 
            Image image = createImage(canvas, m_eventData);
            if (image != null)
            {
                if (m_dragOnSurfaces)
                {
                    m_draggingPlane = transform as RectTransform;
                }
                else
                {
                    m_draggingPlane = canvas.transform as RectTransform;
                }
 
                SetDraggedPosition(m_eventData);
            }
            clearStatus();
        }
    }
}
 
//-------------------------------------------------------------
//! ドラッグ中
//-------------------------------------------------------------
public void OnDrag(PointerEventData _eventData)
{
    if (m_draggingIcon != null)
    {
        SetDraggedPosition(_eventData);
    }
}
 
//-------------------------------------------------------------
//! ドラッグ終了
//-------------------------------------------------------------
public void OnEndDrag(PointerEventData _eventData)
{
    if (m_draggingIcon != null)
    {
        if (m_OnEventPointerEnd != null)
        {
            m_OnEventPointerEnd(_eventData);
        }
 
        Destroy(m_draggingIcon);
        m_draggingIcon = null;
    }
    clearStatus();
}