What's going on with the TOS crew during Discovery? Part.1
To provide some context:
The first episode of discovery takes place in the year 2256
The Enterprise (NCC 1701) launched around 2245. The Enterprise is 11 years old in Discovery and still very much a new starship.
Discovery takes place is three years after the Canon events of the first Original Series pilot and the flashback in the later TOS episode “The Menagerie,” (2253)
During the time of the first Discovery episode Christopher Pike is still in command of the USS Enterprise and is finishing up a 5 year exploratory mission.
Spock is 26 years old and is serving on the USS Enterprise as its science officer.
James T. Kirk is 23 years old and is a Lieutenant aboard the USS Republic. He is finishing his last year in a five year officer training regimen through Starfleet Academy. it will be 9 years till Kirk takes command of the Enterprise.
Nyota Uhura is 17 years old and is more than likely attending classes at Starfleet Academy for advanced phonology and advanced acoustical engineering. She is also a rising star in Starfleet Academy’s Chorale Ensemble. It will be 10 years till she is a Lieutenant assigned aboard the Enterprise.
Montgomery Scott is 34 years old and has been in starfleet for 14 years. it can be assumed that he is serving in an engineering department of a starship or as an engineering advisor for the Deneva colony. it will be 9 years before he is assigned to the Enterprise.