When a character transitions to the Ascended Careers, they have the oppertunity to access increased characteristic increases. However, do they need to do their advances for the previous classes before the +25 and +30? For example, does a newly ascended inquisitor need to purchase the advances for Fellowship from the psyker table, or do the abilities change based on new characteristic advances?

I may have missed it in the rules. Thanks.

I'm reasonably sure the answer is yes, you do have to buy the previous advances. This has to do with how the new characteristic ranks have new terms and I think there is wording that says they're added to the table.