Is it possible to change the style of an Android L TimePickerDialog?

As LordRaydenMK said, use the TimePickerDialog constructor with theme parameter and provide this theme: android.R.style.CustomDatePickerDialog

And in your Styles.xml define this:

  <style name="CustomDatePickerDialog"
         parent="Theme.AppCompat.Light.Dialog.Alert">
    <item name="android:dialogTheme">@style/MyDialogTheme</item>
    <item name="android:timePickerStyle">@style/MyDatePicker</item>
  </style>

  <style name="MyDialogTheme"
         parent="Theme.AppCompat.Light.Dialog">
    <item name="android:timePickerStyle">@style/MyDatePicker</item>
  </style>

  <style name="MyDatePicker"
         parent="@android:style/Widget.Material.Light.TimePicker">
    <item name="android:timePickerMode">spinner</item>
  </style>

Add android:timePickerMode="spinner" to the XML

    <TimePicker
        android:id="@+id/timePicker1"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:timePickerMode="spinner">
    </TimePicker>

https://developer.android.com/reference/android/R.attr.html#timePickerMode

You can choose between spinner or clock modes. This attribute is only available from API level 21, before that the spinner mode was the only option available.

If you want the AM / PM to be a picker instead of a button then I recommend you use the single parameter constructor with a ContextThemeWrapper:

new TimePicker(new ContextThemeWrapper(getActivity(), android.R.style.Theme_Holo_Light_Dialog_NoActionBar));

If you pass the theme into the multiple parameter constructor then you'll end up with a rather ugly AM / PM button, and the colon will be missing between the hour and minute columns.

new TimePicker(getActivity(), null, TimePickerDialog.THEME_HOLO_LIGHT);

You can use the TimePickerDialog constructor with theme parameter to specify the theme.

TimePickerDialog(Context context, 
                 int theme, 
                 TimePickerDialog.OnTimeSetListener callBack, 
                 int hourOfDay, 
                 int minute, 
                 boolean is24HourView)