Try using this.gridRecordNavigationControl1.NavigationBar instead of this.gridRecordNavigationControl1.
using Syncfusion.Windows.Forms;
this.gridRecordNavigationControl1.NavigationBar.ArrowButtonClicked += new ArrowButtonEventHandler(bar_ArrowButtonClicked);
private void bar_ArrowButtonClicked(object sender, ArrowButtonEventArgs e)
{
MessageBox.Show(" Button Clicked");
}