Considering the (assumed) fall of the Romulan Empire due the sun going supernova and the Federation absorbing most of the remnants, the Klingon Empire joining the Federation by the 26 century, and knowledge of other means of space travel (quantum slipstream drive, subspace corridors, etc.) its reasonable that the Federation at some point could potentially reach far, far into the Beta Quadrant, perhaps even 50,000 light years... give or take...
SO... My guess is that there was a major conflict that either shattered or split the Federation, and Discovery just happens to be on the wrong side of the fence.
SO... My guess is that there was a major conflict that either shattered or split the Federation, and Discovery just happens to be on the wrong side of the fence.