Follow this steps
1. Bind your NavigationView with NavigationUI
NavigationUI.setupWithNavController(nav_view, hostFragment.navController)
2. Bind  ActionBar With NavController
NavigationUI.setupActionBarWithNavController(this@NavActivity, hostFragment.navController)
3. Bind ActionBar  and DrawerLayout With NavController
NavigationUI.setupActionBarWithNavController(this@NavActivity, hostFragment.navController, drawer_layout)
4. override  onSupportNavigateUp() in your activity 
override fun onSupportNavigateUp(): Boolean {
    return NavigationUI.navigateUp(drawer_layout, hostFragment.navController) 
              || super.onSupportNavigateUp()
}
Sample:
class NavActivity : AppCompatActivity(), NavigationView.OnNavigationItemSelectedListener {
    lateinit var hostFragment: NavHostFragment
    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_nav)
        setSupportActionBar(toolbar)
        fab.setOnClickListener { view ->
            Snackbar.make(view, "Replace with your own action", Snackbar.LENGTH_LONG)
                    .setAction("Action", null).show()
        }
        val toggle = ActionBarDrawerToggle(
                this, drawer_layout, toolbar, R.string.navigation_drawer_open, R.string.navigation_drawer_close)
        drawer_layout.addDrawerListener(toggle)
        toggle.syncState()
        nav_view.setNavigationItemSelectedListener(this)
        hostFragment = supportFragmentManager.findFragmentById(R.id.my_nav_host_fragment) as NavHostFragment    
        NavigationUI.setupWithNavController(nav_view, hostFragment.navController)    
        NavigationUI.setupActionBarWithNavController(this@NavActivity, hostFragment.navController)    
        NavigationUI.setupActionBarWithNavController(this@NavActivity, hostFragment.navController, drawer_layout)    
    }
    override fun onBackPressed() {
        if (drawer_layout.isDrawerOpen(GravityCompat.START)) {
            drawer_layout.closeDrawer(GravityCompat.START)
        } else {
            super.onBackPressed()
        }
    }
    override fun onSupportNavigateUp(): Boolean {
        return NavigationUI.navigateUp(drawer_layout, hostFragment.navController) || super.onSupportNavigateUp()
    }
    override fun onCreateOptionsMenu(menu: Menu): Boolean {
        // Inflate the menu; this adds items to the action bar if it is present.
        menuInflater.inflate(R.menu.nav, menu)
        return true
    }
    override fun onOptionsItemSelected(item: MenuItem): Boolean {
        // Handle action bar item clicks here. The action bar will
        // automatically handle clicks on the Home/Up button, so long
        // as you specify a parent activity in AndroidManifest.xml.
        when (item.itemId) {
            R.id.action_settings -> return true
            else -> return super.onOptionsItemSelected(item)
        }
    }
    override fun onNavigationItemSelected(item: MenuItem): Boolean {
        // Handle navigation view item clicks here.
        drawer_layout.closeDrawer(GravityCompat.START)
        return true
    }
}
Output
Home Fragment:

Fragment Two:

Fragment Tree:
