Could a character take an alternate rank he qualifies for pre-ascension, post-ascension?

Specifically, could an Imperial Psyker take Tainted Psyker at rank 9, after his transition package, assuming Sactioned Psyker is his new base career?

Technically speaking, Tainted Psyker is a Imperial Psyker only career, and once you've hit Ascension, you are no longer advancing in the Imperial Psyker career, whatever your Ascended career might be. Strictly speaking by that interpretation, anything with a must be Career X requirement can no longer be taken, while anything with a must not be Career Y requirement can be taken.

However, taking alternate ranks after Ascension is something that the rules never actually addressed. As a result, I'd say consult with your GM, and employ common sense.

Personally, however, I'd probably rule a career requirement employs an either/or mechanism for them. If either the pre-Ascension Career qualifies or the Ascended Career is an equivalent to a qualifying pre-Ascension career, then it is considered to match the qualifications.

An Imperial Psyker who, for example, went into the Interrogator career would be able to take an Alt Rank that had a must be an Imperial Psyker requirement, or any other Alt Rank that did not have a Must Not be an Imperial Psyker/must not have a psy rating requirement.

An Adept who went into the psyker talents and Ascended into a Primaris Psyker would be able to take both Adept-only and Imperial Psyker-only Alternate Ranks.

Similarly, a Sororitas Character who Ascended into Interrogator or Inquisitor would still be counted as being a Sororitas for being allowed to take or not allowed to take alternate ranks, ie, no Warp-Dabbler for her.