SO 9001:2015 instead of “outsourced process” promotes the wording “externally provided processes”.
You don’t need to draft an externally provided process. The process is owned and operated by an outside party, what you need is to develop a systematic way to control that process. A process is not a product, so the focus should be on specific process parameters rather than on product characteristics.
Define mutually recognized and accepted tailor-made service level parameters, as well as monitoring methodology, reporting, and follow-up actions. Those parameters and monitoring methodology should depend on the business risk associated with the service got from an outsourced organization, so they definitely must be customized according to the organization or the types of services needed.
What you can draft is how that externally provided process is going to be controlled and monitored:
What documents need to be created and signed to set service level parameters, roles, responsibilities, and authorities for monitoring, reporting, and consequences?
What procedures will be followed? Who will create them? Who will ensure that the outside party is trained on them?
Who is going to control, what and with what frequency?
What records will be filled and by whom?
Who should act in case of doubts or nonconformities?
Will second party audits take place?
To learn more about externally provided processes you can see these articles: