>> IRDA has described on its website:

FAQ on Ombudsman Scheme

21) Is there any appeal against a decision given by the Ombudsman?

No, as the Recommendation or Award of the Insurance Ombudsman are both subject to acceptance by the complainant in full and final settlement of the complaint. If such acceptance is not agreeable, the complainant may exercise the right to take recourse to the normal process of law against the insurance company. Further, dismissal of a complaint by the Insurance Ombudsman does not vitiate the complainants’ right to seek legal remedy against the insurers complained against, as per normal process of law.

https://www.policyholder.gov.in/FAQ_on_Ombudsman_Scheme.aspx

>>  The verdict given by the insurance ombudsman is binding on the insurance company.

The company can not   appeal against the order of the insurance ombudsman. However the individual complainant , if not satisfied with the verdict  can approach the courts. 

You may also go thru and pursue: Redressal of Public Grievances Rules, 1998 which are available at the website of IRDA too:

https://www.policyholder.gov.in/RPG_Rules_concerning_Ombudsman_scheme.aspx

and

https://www.niapune.com/pdfs/Bimaquest/vol11-issue1/Deepa%20Sharma.pdf

>> The National Commission declined to accept the contentions of the insurance company that:

 “ombudsman's role was quasi-judicial in nature’:

 “repudiation of the claim the complainant ......................before the Insurance Ombudsman and the same was rejected after considering the evidence in detail, hence the complaint before the District Forum under Consumer Protection Act was not maintainable. ‘

And has held that

“Analysing the various provisions of the RPG rules, the national commission held that the ombudsman is appointed by the government and the industry, and his role is to act as a counsellor and a mediator. If mediation fails, then he can make an award which he thinks is fair. The insurer is then bound to comply with it, only if the consumer agrees to accept it. Thus, it is up to the consumer to choose whether or not to accept the award.

“

“it is held that the decision of the Ombudsman is not binding on the complainant and the decision of the Insurance Company to repudiate the claim is subject to adjudication by the Fora Constituted under the Consumer Protection Act.’

“Consumer Fora has jurisdiction to decide a matter which has already been decided by 'Ombudsman' appointed under the Redressal of Public Grievances Rules, 1998 framed under Sub-section (1) of Section 114 of the Insurance Act, 1938.’

Kamleshwari Prasad Singh v/s National Insurance Company Ltd

https://indiankanoon.org/doc/1574994/

Attached:

Kamleshwari Prasad Singh v/s National Insurance Company Ltd