Recently installed new rotors and pads on front and rear.
After few weeks driving, heard bad sounds from brake system.
Finally got wheel off and the rotor has been gouged by a stone/pebble
that got caught between the pad and rotor.
Rather than replace or turn a brand new rotor, have decided to run it
until next brake pad change then have it turned.
Would there be any issues in waiting til next pad change to have the rotors machined?

 

No idea based on no details given. Hard to imagine a “pebble” fitting between the pad and rotor, the clearance is very small. It would depend on exactly where the gouge is and how big/deep it is. Turning may not be an option if too deep. It is “probably” okay to keep driving as-is.

 

Yeah it didn't gouge it very deep. It was a very tiny pebble about the size of rock salt that was stuck on the pad. Somehow it must of got kicked up when I was traveling the back gravel roads. Figure I'll just wear the rotors down for now. Would be a waste to have new rotors turned.

 

While common it does happen and more often then many think. In most cases you can continue to use the existing pad and rotor but that would be the decision between the service technician and yourself.
Expect to hear noises and may even feel some vibration during hard or sustain braking.