If a prior service female enlists and gets pregnant during her new AIT, is she allowed to continue?

How did she find out she was pregnant? Has she been to sick call? She will need to see a military doctor to confirm the pregnancy and get a profile. Depending on if the SM is married or not and the branch of service (AD, USAR, NG) the command may give the SM the option to get out (chapter), come back after the pregnancy or continue the course if early on in the pregnancy. There are some other legal options if the Soldier violated an order or policy.

AR 135-178, 6-3.
When it has been determined that a Soldier became pregnant after enlistment, she may elect one of the options under the provisions of AR 135–91, except as follows:
a. Discharge for pregnancy. Upon her request, a Soldier who meets all of the following criteria will be discharged from military service when it has been determined that the pregnancy occurred after she was processed for enlistment:
(1) She has not entered on initial active duty for training (IADT) or ever completed IET.
(2) She has not incurred an active duty obligation as a result of a federally subsidized program

I'm not sure with AIT - I believe they started to let women go to schools pregnant. This is what Army Directive 2022-06 states on PME:

e. Professional Military Education (PME).
(1) Temporary profiles for fertility/pregnancy/postpartum will not restrict the
eligibility for officers and warrant officers to attend and/or graduate from PME (such
SUBJECT: Army Directive 2022-06 (Parenthood, Pregnancy, and Postpartum) as Basic Officer Leaders Course (BOLC)–B, Captain Career Course, Command and General Staff Officer College, Army War College, Warrant Officer Basic Course (WOBC), Warrant Officer Advanced Course, Warrant Officer Intermediate Level Education, and Warrant Officer Senior Service Education). Nor will such temporary profiles restrict the eligibility for noncommissioned officers (NCOs) to attend the Sergeants Major Course (or equivalent course). The following provisions apply to the pregnant and postpartum
officers, warrant officers, and NCOs attending the courses identified in this paragraph:
(a) These Soldiers are exempt from record physical fitness testing in accordance with paragraph 4b of this directive. The most recent record physical fitness test will be used to satisfy PME eligibility and graduation requirements. Soldiers who do not have a passing physical fitness test of record dated within the last 730 days (24 months) must receive a waiver from the school’s commandant.
(b) Medical Clearance. Pregnant Soldiers will be cleared, in writing, to attend PME by a healthcare provider. Postpartum Soldiers through the end of their postpartum profile (normally 42 days) will be cleared, in writing, to attend PME by a healthcare provider. Soldiers who are no longer on a postpartum profile do not require medical clearance.
(c) A pregnancy profile will not disqualify a Soldier from being selected as an honor graduate or commandant list selectee.

I mean that seems to apply to officers and SGM Academy...it says it applies to pregnant or postpartum officers, WOs or NCOs attending the courses identified in the paragraph and it doesn't identify AIT or any NCOES PME.

She needs to go get it verified at the MTF and then notify whoever is in charge of the prior service people. I know they have nothing to do with the drill sergeants. The instructors or senior instructor perhaps? I don't think she can continue while pregnant based on the Army Directive published last year.

She will need to go through medical and check all of the required boxes to start the process. I recommend just staying out of it and letting the process MAJ Bethany Garbarini outlined take it's course.