Moogle, I appreciate your interest. However, being a GM also involves looking out for you, so, I'll make the following observations:
1- It looks like you're in downtime, but would it make sense for Kyoka to just up and leave like this? SAINT isn't going to order her off her present assignment, after all. Excuses can be made, but we need to make sure this feels coherent for your sake, the sake of the people you leave behind, and the sake of the new characters you'll get to roleplay with.
2- Are you sure this is the best career path for her? She looks like Aeon's highest ranked PC. This gives you unique opportunities you may not find on Byakuren.
3- You don't have a lot of active alts. In fact, Kyoka appears to be 'your main'. Infantry combat can be pivotal in my plots, but it's also infrequent. If you have an knack for promoting your own roleplay and keeping busy, you might manage. But I'm a little scared of you ending up being bored due to your dedication to this character. Most other infantry characters involved are from people with their thumbs in multiple stories already.
...
This said, we can find ways to involve Kyoka. The key is her being 'free'. One good way of doing that is to have her go back to school.
She's an Heisho. NCOs usually get leadership classes and such. If she hasn't done so yet, if could be her window to do so.
Or... she's an Itto Heisho. That's just before being a Juni. She could be testing out for a 'speciality' to earn her Juni rank.
Either way, SAPM could note her file and her notable service record, and submit it to SAINT's attention - giving her the window to make her involved.