I searched, downloaded and read the rules in the Big 12 about transferring within the conference:
6.3 Intraconference Transfers. The eligibility of a student-athlete who transfers directly or indirectly from one Conference Member Institution to another shall be determined by NCAA regulations and the following Conference requirements. In the event NCAA regulations require the student-athlete to complete one full academic year in residence before being eligible to compete in a sport, the student-athlete shall also forfeit one season of competition in that sport. The waiver of a NCAA transfer regulation for a student-athlete does not negate the need for a waiver of this section.
6.3.1 4-2-4 Transfers. A 4-2-4 transfer student-athlete who is in compliance with NCAA Bylaw 14.5.6 must complete one full academic year in residence before being eligible to compete in a sport and forfeit one season of competition unless, in sports other than football or basketball, the director of athletics of the Conference Member Institution of initial enrollment consents in writing to the student-athlete’s enrollment at the second Conference Member Institution. Any consent given relating to the indirect intraconference transfer may be unconditional or conditioned on the student-athlete completing one full academic year in residence at the second conference Member Institution before competing.
So you have to sit out one year and you lose one year of eligibility (redshirt won't help) IF you play in football or basketball.