[Python] How to update a CSV file based on certain condition to get the new value only if that...

I have been working on this for a couple of hours, I want to update the CSV file only when the new score is higher than the current score. Let's say the first time I played the game, I got a score of 10 and the next time I got a score of 5, I just want to update the 10 only if the new score is higher than 10. But when I tried it is still update the file even when the new score is lower than the current score and I don't want that to happen. Could you look at the code below and give me some int so I can make that work please? This is Just a part of my code, if the entire code will be needed to help me with that please let me know. I was creating the game using OOP concepts.

from turtle import Turtle
import csv

class ScoreBoard:
def __init__(self):
self.score = 0
self.new_score = 0
self.text_score = Turtle()
self.text_score.hideturtle()
self.text_score.penup()
self.text_score.goto(200, 260)
self.text_score.color("white")
self.update_score()

def update_score(self):
self.text_score.clear()
self.text_score.write(f"Score: {self.score}", align="center", font=("Arial", 20, 'normal'))

def increase_score(self):
self.score += 1
self.text_score.clear()
self.update_score()

def game_over(self):
self.highest_score()
self.text_score.goto(0, 0)
self.text_score.color("red")
self.text_score.write(f"Game over!\nYour highest score is: {self.score}", align="center", font=("Arial", 20, "normal"))

def highest_score(self):
if self.score > self.new_score:
self.new_score = self.score
try:
with open("score.csv", "w") as file:
data = file.write(str(self.new_score))
self.text_score.write(f"Score: {data}", align="center", font=("Arial", 20, 'normal'))
except FileNotFoundError:
with open("score.csv", 'w') as file:
file.write(self.score)
self.text_score.write(f"Score: {self.score}", align="center", font=("Arial", 20, 'normal'))
self.text_score.write(f"Score: {self.score}", align="center", font=("Arial", 20, 'normal'))

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