Can counter claim submit to 2nd Arbitrator if GOVT fails submit to 1 Arbitrator?

Dear Client,
As the Limitation Act is made applicable to Arbitrations, in the case of a counter claim by a respondent in an arbitral proceeding, the date on which the counter claim is made before the arbitrator will be the date of “institution” insofar as the counter claim is concerned. Section 43 of the Arbitration and Conciliation Act, 1996 expressly provides for the application of the Limitation Act to arbitral proceedings. In the matter of Ashok Kalra v. Wing Commander Surendra Agnihotri, the Hon’ble Apex Court after careful consideration of the contents of Order VIII Rule 6A CPC held that the counter claim, if any is to be filed by the Respondent, it needs to be filed before the framing of issues and not after that. In arbitration proceedings as well, the Respondent is allowed to bring a counter claim against the Claimant. So far the period of limitation of a claim or a counterclaim is concerned, the Supreme Court’s judgment in State of Goa v. Praveen Enterprises15 makes the law very clear. In respect of claims in arbitration, the Court clarifies by a combined reading of Section 21 of the Arbitration Act, and Section 3 of the Limitation Act, 1963. Accordingly, you may consult the matter with an Advocate for further clarifications and steps.

Dear client,
If they haven't intimated about the arbitration proceedings, then it is void.
In the case of National Highway Authority of India Vs Transstroy (India) Limited (Supreme Court) it was held that the counter-claim of a party cannot be rejected for the simple reason that the claims were not notified prior to initiating arbitration.