What is Tracking Area Update Reject in LTE?

It is the EPS NAS message the network sends when the tracking area updating procedure is rejected.

What should I inspect first in Tracking Area Update Reject?

Start with the EMM cause, then inspect any returned T3346, T3402, T3448, or forbidden-TAI information.

Why is Tracking Area Update Reject important in troubleshooting?

Because it explains not only that the TAU path failed, but also which reject branch and retry behavior the UE is expected to follow.

What usually comes after Tracking Area Update Reject?

That depends on the returned cause and timers: the UE may wait, retry later, or move into attach or broader recovery handling.