Regularisation of contractual employees

Let her (your wife) submit representation to authorities concerned to consider her case sympathetically.

Yes, your wife can submit a representation. If no positive result, she has the option for seeking judicial review. However, discretion of the Court/Tribunal is limited in such matters involving issues/questions of public policy.

As the government notification specifies "current" contractual employees, your wife faces an administrative hurdle since her contract was not renewed in 2023. However, given her 10 years of long-standing service, she has strong grounds to seek inclusion.

As per notification see  if the eligibility is defined by a specific cut-off date (e.g., "working as of [Date]") or total cumulative years of service. Check if the policy has clauses condoning temporary breaks or non-renewals for former contractual staff. Ensure there are provisions relaxing upper-age limits or granting bonus marks for candidates with past contractual experience.

If the DISCOM rejects her representation or if the online application portal does not allow former employees to apply, her primary remedy is to approach the State High Court by filing a Writ Petition under Article 226 of the Constitution. You can argue before high court stating that excluding n employee who served 10 years while allowing those with far less service (simply because they are currently on roll) is arbitrary and discriminatory.

You can also can pray for an interim direction from the High Court ordering the DISCOM to allow her to appear for the test provisionally, keeping her result in a sealed cover pending the final verdict. 

It would be better to contact, consult and engage a local prudent lawyer practicing service matters for proper analyses of facts / documents, professional advise and necessary proceeding.