Why is this python script running in background consuming 100 % CPU?

You forgot the time.sleep() in your while loop, according to this answer on SO sleeping for 0.2s is a good compromise between polling frequency and CPU load:

import time

while True:
  get_clipboard()
  time.sleep(0.2) # sleep for 0.2 seconds

Checking the clipboard every 0.2 seconds seems easily often enough; if you want less CPU load you can even increase this value – few users change the clipboard content from one second to another.

Note that in general polling in a loop as often as that is not considered good design. A better approach would be to act on the event of changing the clipboard content, an example for GTK can be found in this SO answer.

Further reading

• linuxconfig.org article on Python While Loops
• cyberciti.biz article on time.sleep()
• blog article on How To Make Python Wait discussing different ways, some of which are much more elaborate and flexible than the static time.sleep()

I finally make it work a without loop. This is the code:

I had to install few modules: sudo apt install python3-gi python3-gi-cairo gir1.2-gtk-3.0

#!/usr/bin/env python3
import gi, sys
gi.require_version('Gtk', '3.0')
from gi.repository import Gtk, Gdk

last_clipboard = ""

def callBack(*args):
  global last_clipboard
  new_clipboard = clip.wait_for_text()
  if new_clipboard != last_clipboard:
    last_clipboard = new_clipboard
    print("new Clipboard")
    print(new_clipboard)

clip = Gtk.Clipboard.get(Gdk.SELECTION_CLIPBOARD)
clip.connect('owner-change',callBack)
Gtk.main()

feel free to choose the solution that fits for you.

You are running the thing in a while True: loop! That means that the CPU is constantly running your loop. Just add a small pause there and you should see the CPU usage drop precipitously:

#!/usr/bin/env python

import Tkinter
import time

last_clipboard = ""

def get_clipboard():
  global last_clipboard
  root = Tkinter.Tk()
  root.withdraw() # Hide the main window (optional)
  text_in_clipboard = root.clipboard_get()
  if text_in_clipboard != last_clipboard:
    last_clipboard = text_in_clipboard
    print last_clipboard

while True:
  get_clipboard()
  time.sleep(1)