How do I drive 14.3Mhz clock input from 10MHz?
What you need is a PLL, a phase-locked loop. It works by comparing one oscillator that you can control, with a reference oscillator. The trick is that it is easy to divide the frequency of an oscillator using a digital counter, so what you do here is to divide the 14.3 MHz oscillator by 143, the 10.0 MHz reference by 100, and then use the output from this comparison to make sure that the 14.3 source is running at an exact relation to the stable 10 MHz reference.

There are numerous circuits that can do all of this in one package, sometimes even including a reference oscillator. It is very common having to synthesize frequencies from a stable oscillator, so these are not unusual.