What happened to Jaeger who was after Tak in Altered Carbon? He was looking for Takeshi after Tak killed some CTAC officers and escaped with Rei. We can see Jaeger was there in the forest where they killed almost all the Envoys.
We don't know
We know very little about Jaeger other than that he is/was a CTAC Praetorian and led the assault force that eventually arrested Takeshi Kovacs.
Essentially, having captured Kovacs, his job was done and, presumably, he carried on with his current position.
Whether he has survived the intervening 250 years between Kovac's capture / imprisonment and the events in "current time" Altered Carbon is open to question.
It's possible he's still around (re-sleeved etc.) but we just have no information on this.