Is it ever explained how Karen/Michelle ended up in the IAA?

On GTA IV, Karen was coerced by Agent ULP to follow and track Niko. On GTA V, she is a high level IAA agent as seen on the mission "Three's Company".

Is it ever explained how did she end up in the IAA?

While it is explicitly never explained in game, United Liberty Paper is a front for the International Affairs Agency, so one reasonably can assume that she was Karen was promoted to her current role during the five years between the two games.

Karen's role as a government agent also explains her continued activities in both GTA V story and GTA Online where she assists in the Humane Labs raid and has knowledge of the Fleeca Bank heist.

From ULP's Wikia page proving it's an IIA front:

IAA Front :

In the game's files, U.L. Paper's missions are titled "CIA", i.e., the Central Intelligence Agency. Several framed documents on the contact's office walls carry the seal of the CIA. In addition the internal model of U.L. Paper is called ..._cia. Furthermore the compass on the first floor resembles the one on the CIA seal. Another piece of evidence that suggests that U.L. Paper is an IAA/CIA front is the U.L Paper contact's expression of dislike for the FIB, saying to Niko that he will hand him over to the 'cretins in the FIB' if he doesn't do as he is told.

It is later revealed in Grand Theft Auto V that both Agent ULP and Karen are IAA agents and United Liberty Paper was clearly an IAA front company in Liberty City.