I have problem with tkinter mainloop inside a while loop

You wanna display Helsinki-Finland weather via www.foreca.com, but It is a bad approach, you just froze your app for 10 seconds in each loop.

time.sleep(10)  # freeze for 10 secs

Eliminate the while loop and use root.mainloop() instead, Then your app stays running, up to user close the app by clicking on x button.

from selenium import webdriver
from selenium.webdriver.common.keys import Keys
import time
from tkinter import *

selain = webdriver.Chrome()
selain.get("https://m.kellonaika.fi")
kello = selain.find_element_by_id("clock-time")
selain.get("https://www.foreca.fi/Finland/Salo")
sää = selain.find_element_by_class_name("l")
sää1 = selain.find_element_by_class_name("r")
print(sää.text)
print(sää1.text)
root = Tk()
myLabel1 = Label(root, text="sää salossa nyt")
myLabel3 = Label(root, text=sää.text)
myLabel4 = Label(root, text=sää1.text)
myLabel1.grid(row=0, column=2)

myLabel3.grid(row=2, column=1)
myLabel4.grid(row=3, column=1)

selain.close()
root.mainloop()

But You should use threading to update the Tkinter form, to keep update and refresh data. like:

# run the while loop in a thread
Thread(target=refresh_data, daemon=True).start()

Which refresh_data() is a function

You should move the tkinter code out of the while loop and run the while loop in a thread:

from selenium import webdriver
#from selenium.webdriver.common.keys import Keys
from selenium.webdriver.chrome.options import Options
import time
from tkinter import *
from threading import Thread

root = Tk()

# labels for the result
myLabel1 = Label(root, text="sää salossa nyt")
myLabel3 = Label(root, justify='left')
myLabel4 = Label(root, justify='left')

myLabel1.grid(row=0, column=0)
myLabel3.grid(row=2, column=1, sticky='w')
myLabel4.grid(row=3, column=1, sticky='w')

def get_data():
    # using headless mode
    options = Options()
    options.add_argument("--headless")
    selain = webdriver.Chrome(options=options)
    while True:
        selain.get("https://m.kellonaika.fi")
        #kello = selain.find_element_by_id("clock-time")
        selain.get("https://www.foreca.fi/Finland/Salo")
        sää = selain.find_element_by_class_name("l")
        sää1 = selain.find_element_by_class_name("r")
        # show the result
        myLabel3.config(text=sää.text)
        myLabel4.config(text=sää1.text)
        print(sää.text)
        print(sää1.text)
        time.sleep(10)
    selain.close()

# run the while loop in a thread
Thread(target=get_data, daemon=True).start()

root.mainloop()