Should we replace Action Bar by ToolBar?

Yes, you should replace ActionBar with new toolbar.

Reasons

1. It looks modern and it follows new material design.

2. Unlike Action bar, toolbar is not part of window decor. You define it and place it just like any other widget… therefore, you have freedom to place it anywhere in the parent layout.

3. You have freedom to put any widget inside toolbar.

4. You can define multiple toolbars.

EDIT

What i meant is you can place other widgets (views) inside toolbar.

Create a separate layout file for the toolbar (good for reusability). In my case file name is main_toolbar.xml

<?xml version="1.0" encoding="utf-8"?>
<android.support.v7.widget.Toolbar
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    xmlns:App="http://schemas.android.com/apk/res-auto"
    xmlns:segmentedgroup="http://schemas.android.com/apk/res-auto"
    android:id="@+id/toolbar"
    android:layout_width="match_parent"
    App:theme="@style/ToolbarColoredBackArrow"
    android:layout_height="56dp"
    android:background="@color/primary_color" >

    <TextView
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:textSize="@dimen/drawer_fntsize"
        android:text="Title"
        android:id="@+id/lbl_title"
        android:textColor="@color/title_text_color"
        android:layout_gravity="center" />

 </android.support.v7.widget.Toolbar>

Then include this toolbar in your main layout like this

<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <include
        android:id="@+id/toolbar"
        layout="@layout/main_toolbar" />

    <FrameLayout
        android:id="@+id/content_frame"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:layout_below="@+id/toolbar" />

</RelativeLayout>

As you can see in this example i placed TextView inside the toolbar