You're looking for the r+ or a+ mode, which allows read and write operations to files (see more).
With r+, the position is initially at the beginning, but reading it once will push it towards the end, allowing you to append. With a+, the position is initially at the end.
with open("filename", "r+") as f:
# here, position is initially at the beginning
text = f.read()
# after reading, the position is pushed toward the end
f.write("stuff to append")
with open("filename", "a+") as f:
# here, position is already at the end
f.write("stuff to append")
If you ever need to do an entire reread, you could return to the starting position by doing f.seek(0).
with open("filename", "r+") as f:
text = f.read()
f.write("stuff to append")
f.seek(0) # return to the top of the file
text = f.read()
assert text.endswith("stuff to append")