If the IT service provider has an ISO 27001 or SOC2 certification, it is a good starting point, but it is not a substitution for DORA compliance. To avoid doubt, those certifications are voluntary and open to broad interpretation, while DORA is a law.
The good news is that the DORA technical requirements, highlighted in the respective draft RTSs, use the security industry's best practices. Such an alignment can and should utilise existing processes, hopefully already existing within an organisation.
Based on the suggested RTSs, the bad news is that the controls' requirements are much more detailed. Those details will require an additional implementation and management effort.
The IT service provider designated as critical can expect more scrutiny from financial clients, starting with new contract clause negotiation covering additional compliance requirements and subcontractors’ information. Also periodic status reporting about vulnerability management, client-specific incident reporting regimes, and resilience testing will be required.