Can I simulate a clock without an RTC connected?
TimeLib.h has a virtual clock that can be updated and corrected from multiple sources, including an RTC chip or an NTP server on the internet (assuming an internet connection).

It doesn't need that clock source, though, but it will drift with time. Once you have set the clock correctly it will keep close to the right time (assuming no reset or power loss of the Arduino). Not perfect (because the Arduino's main clock isn't perfect) but close enough for many simple applications.