What is Extended Service Request in LTE?

It is the EPS NAS message the UE sends when the service request procedure needs the extended service-type form instead of the basic Service Request message.

What should I inspect first in Extended Service Request?

Start with Service type, because that field explains why the UE used the extended service branch.

Why is Extended Service Request important in troubleshooting?

Because it tells you which service-restoration branch the UE actually asked the network to continue, especially in CS fallback and packet-services-via-S1 cases.

What usually comes after Extended Service Request?

The network may continue with authentication or security procedures, then either accept the restore path with Service Accept or reject it with Service Reject.