The approver is a special user picker field in Jira Service Desk. In most cases where it's used, a service desk customer has to select an approver account. This is just a jira user account. So if you were looking to change the email address for that account, it's not actually something that would change within the project, but rather this is a change to the user account itself in Jira.
If that is the case, then a Jira system admin could go to to Gear Icon -> User Management. If this user exists in the Jira Internal directory that admin could change the email address for that account.
However I can't help but think that your environment might be different than what I am thinking here. When a service desk customer creates a request that requires approval, are they selecting the user account in the customer portal? Or not? If not, then perhaps we can investigate some alternatives to my first approach here.
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