ASR has a few billable line items like the protected instance count, Storage, Storage transactions and outbound data transfers. The primary unit is the number of protected instance which refers to the VM which is replicated to the DR site. There is different pricing when the DR site is either a secondary DC or Azure.
During a disaster scenario when the replicated vm images are brought in to life as virtual machines, then the customer will incur compute cost apart from the other cost components mentioned earlier.
Refer to the link here for the details of the billable components for ASR.