Unless your ticket class permits rescheduling for free (unlikely unless you've booked a more expensive flexible fare class), because these flights will be on two separate tickets, you are owed no protection if the first flight is delayed.
- Book the second flight with a very long delay (a few hours) to maximize the odds of you arriving on time.
- Modify the original booking to add the flight connection to the second city. The airline will then owe you a guarantee of passage to the second city, if you miss the second flight due to the first being delayed.
- Book the second ticket as a flexible ticket, so that if it is apparent you will be late, you can reschedule it for little or no cost.
You could possibly use a lower fare class on the second ticket, but you will have to pay a fee to reschedule the flight, and if you don't do so prior to the departure of your second flight, you may end up forfeiting the entire fare.