NIST's Cybersecurity Framework (CSF) 2.0 has a Continuous Monitoring category (DE.CM). It covers monitoring assets to find anomalies, indicators of compromise and other potentially adverse events, which is the job of security monitoring, whoever runs it. The other sense, checking that controls keep working and producing evidence, is compliance work.
NIST SP 800-61 Rev. 3 lists outsourcing a security operations center to a Managed Security Services Provider (MSSP) as one way to staff incident handling, and notes that such a provider can take a primary role in detecting, responding to and recovering from incidents.