If a new DataRow is added to the DataTable during runtime, how can we trigger the update?

You need to call this.autoComplete1.SetTableData() method which sets the internal table data based on the AutoComplete control's DataSource property.

C#

DataTable dt;
private void Form1_Load(object sender, System.EventArgs e)
{
    dt=new DataTable("select");
    dt.Columns.Add("Countries");
    dt.Columns.Add("states");
    dt.Rows.Add(new object[]{"NorthCarolina" });
    dt.Rows.Add(new object[]{"India " });
    dt.Rows.Add(new object[]{"New York " });
    dt.Rows.Add(new object[]{"Washington " });
    dt.Rows.Add(new object[]{"London"});
    dt.Rows.Add(new object[]{"Canada"});
    autoComplete1.DataSource=dt;
}

private void button1_Click(object sender, System.EventArgs e)
{
    dt.Rows.Add(new object[]{"new1"});
    dt.Rows.Add(new object[]{"new2"});
    //sets the internal table data based on the AutoComplete.DataSource property.
    this.autoComplete1.SetTableData ();
}

VB

Private dt As DataTable

Private Sub Form1_Load(ByVal sender As Object, ByVal e As System.EventArgs)
    dt = New DataTable("select")
    dt.Columns.Add("Countries")
    dt.Columns.Add("states")
    dt.Rows.Add(New Object() {"NorthCarolina"})
    dt.Rows.Add(New Object() {"India "})
    dt.Rows.Add(New Object() {"New York "})
    dt.Rows.Add(New Object() {"Washington "})
    dt.Rows.Add(New Object() {"London"})
    dt.Rows.Add(New Object() {"Canada"})
    autoComplete1.DataSource = dt
End Sub

Private Sub button1_Click(ByVal sender As Object, ByVal e As System.EventArgs)
    dt.Rows.Add(New Object() {"new1"})
    dt.Rows.Add(New Object() {"new2"})
    Me.autoComplete1.SetTableData
End Sub