Will Cervical disc herniations in later stages lead to instability?

Not very likely. They are more associated with pain than with instability (I am interpreting ‘later stages’ in your question to mean ‘severe disc herniations’ or ‘untreated disc herniations’).

Disc herniations, together with stenosis of the neural foramen, are alleged to be the primary cause of radicular pain presentations that can be traced to the spine. Vertebral displacements on the other hand, such as spondylolisthesis or retrolisthesis (backward slippage), with or without disc affectations, significantly affect the spinal architecture and are more likely to progress or lead to spinal instability in ‘later stages’ than disc herniations.