NTP Clock on a Raspberry Pi
In general your script looks good when considering the style and structure, but there are a few issues:


Strange name for check_ntp_time – This holds the time since the last time you did time.time(), and in reality is a temporary variable for when you need to check it the last time. It doesn't convey the real purpose of the variable.

I would rather do time_to_check_ntp = time.time() + 86400, and let the condition be time.time() &lt; time_to_check_ntp or similar, which reads easier as to whether we've come to that time already, or not. 
Consider replacing toilet with python stuff – One option could be to use pyfiglet, and another could be to use fonts of your own based on script suggestions from "Is there a python library that allows to easily print ascii-art text?" and "ASCII Art With Letters".
New function for setterm &amp; clear – Introduce a new function where you can set it to on or off, which would remove some repetition of code.
Replace call to date to get date with datetime module – In general I would like for python script to do most of it using python stuff. Some of it like clear and setterm, or setting the date needs to be done in the shell on the terminal, so some can't be avoided, but stuff like getting the date I think should be done using internal tools, if possible.
Avoid the recursivity – Both display_clock() and get_ntp_time() calls each other causing a bad recursivity. If you change display_clock to have a while True: loop you could have a if time.time() &gt; time_to_check_ntp: which then calls get_ntp_time() which possibly should be named correct_time_using_ntp(), and sets a new time_to_check_ntp. 
Remove output before clearing the terminal – No point in outputting text straight ahead of a terminal clear. Nobody would be able to catch these message, unless something fails. I would remove it, or add a logger to keep track of the history of the script.


I'm not going to propose new code, as I don't have the ability to test it, but I hope my suggestions are meaningful and you see how to implement it. If not, please do comment.