ITSM and Agile are two different methodologies which complement each other well. ITSM encompasses the whole life cycle of the service, and Agile is used (mainly) while implementing a new service or changing an existing one (as one-off activity or as continuous delivery).
However, there are some specifics, like:
1. ITSM is used to e.g. define business and or customer requirements, define IT(SM) strategy, manage risks, manage service portfolio and service catalogue, manage the financial aspect of ITSM, manage information security, etc.
2. Agile is used as project delivery approach – new services are handled as a project as well as (some, e.g. bigger) change implementation on existing services. Or implementation of improvement initiatives.
3. ITSM activities are important while service is in a live environment – e.g. to handle incidents, service requests, problems or to measure and monitor, etc.
4. Agile can be used to respond to changes in the environment where IT services are delivered
And there are many more.
So, as you can see, there are many touchpoints between ITSM and Agile. Successful implementation of both can significantly influence IT service delivery and, consequently, customer satisfaction.