One of the pre-requisites for Teams (online) integration with Exchange on-premise calendars is oauth authentication.
Sometimes solution providers just install a single or multiple Exchange 2016 servers to ensure the oauth pre-requisite is delivered. However if the project scenario requires Exchange on-premise mailboxes to be migrated as quickly as possible to Exchange Online then it may seem overkill to implement Exchange 2016 servers during this transition period.
Exchange 2013 CU24 and above does not complete the oauth authentication part of the Hybrid wizard, however Microsoft do have an article on how to configure OAUTH for Exchange 2013.
Configure OAUTH for Exchange 2013 :
This solution works perfectly and allows an organization to transition from Exchange 2013 to Exchange Online without the requirement for Exchange 2016 servers and enables Teams to interact with Exchange 2013 on-premise calendars.