Is it possible to get a slot to reclassify to 31K?

As a reclass, be prepared to wait a while. It's hard enough to get a slot when enlisting in the first place and out of my class of 24 right now (biggest class they've ever had btw) there's only 4 inserts and one of them is NG. I just got lucky and hardballed my recruiter saying I wasn't gunna join till a 31K slot opened up and waited till it did. They can't save slots for this MOS, theres either a slot open when they look or there isn't.

First, your Career Counselor is the person you reclass through, if they say there are no slots, then you can't reclass into that. I haven't seen any slots since they first created the MOS years ago and only 31B were allowed to reclass into it.
Second, 31K is not an application MOS as other people suggested. There's no packet for it, the slot exists or it doesn't. HRC holds the majority of training seats for IET students and only a few go to prior service.
Your Career Counselor is the subject matter expert when it comes to reclass. I would avoid asking the internet because you'll get a lot of misinformation and straight bad data. It's a highly technical area and the seats change daily. If you feel your counselor isn't telling you everything you can go to the Senior Career Counselor at the brigade and ask them.

There’s actually a Mil-per message out for this mos right now if you look on HRC. It’s open to applications.