Can I get a new ARN along with TRN if I apply GST for the second time?

TRN is Temporary Reference Number which is generated on successfully submission of PART-1 while submitting application for GST registration. TRN number is used to open PART-B in GST registration and also to login in GST registration application.

What is ARN?

ARN is Acknowledgement Reference Number which signifies successful submission of GST application while submitting application for GST registration and which is generated on submission of PART-B.

With respect to your question cited, you will get new ARN with TRN if you will apply for GST registration second time and that ARN number you can use to track your application status.