Scroll rect with mouse locked

You'll need to modify your scroll class or create a class to handle the scrolling and use it to handle input received and pass the scroll amount/direction to your scroll view object. Something like

 public ScrollRect scrollRect;
 public float speed;
 public KeyCode Up, Down;
 void Update()
 {
     Vector2 velocity = Vector2.zero;
     if (Input.GetKey(Up))
     {
         velocity = Vector2.up * speed;
     }
     else if (Input.GetKey(Down))
     {
         velocity = -Vector2.up * speed;
     }
     scrollRect.velocity = velocity;
 }