The rules for advanced specialties in Hammer of the Emperor say that your original specialist equipment is replaced with the new list in your advanced specialty. How does this work with augmetics? For instance, if I were a Tech-Priest that chose to become a Crimson Exemplar, would I lose the MIU and mechadendrite that I originally received?

Only War Living Errata , page 38:

Question : If a character takes an Advanced Speciality (or switches to another Speciality) (see page 52 of Hammer of the Emperor), does he have to return any Cybernetics that were part of his previous set of Specialist Equipment?
Answer : Although the character’s Specialist Equipment changes when he takes an Advanced Speciality (or switches to another Speciality), typically, he would not be required to return any Cybernetic Replacements or Implant Systems he received from his previous Speciality or Advanced Speciality’s Specialist Equipment due to issues of logistical impracticality. However, if his cybernetics become damaged or are destroyed, he might find it more difficult to replace them, as they are no longer part of his Specialist Equipment.

Thank you, I'll be sure to check errata in the future.