Edit the Contact Roles for Account, Case, Contract, or Opportunity objects

The Contact Roles related list of an Account, Case, Contract, or Opportunity displays the roles that each Contact or Person Account plays in that record. On the Person Account detail pages, the Opportunity Contact Roles related list displays the Opportunities on which the Person Account is listed in the Account Name field of the Opportunity.

To edit the Contact Role picklist values perform the following:

In Classic:
Go to Setup | Customize | Accounts | Contact Roles on Accounts
Go to Setup | Customize | Contracts | Contact Roles on Contracts
Go to Setup | Customize | Cases | Contact Roles on Cases
Go to Setup | Customize | Opportunities | Contact Roles on Opportunities

In Lightning:

Click the Gear Icon then go to  Setup | Feature Setting | Sales | Contact Roles on Contracts
Click the Gear Icon then go to Setup | Feature Setting | Sales | Contact Roles on Contracts
Click the Gear Icon then go to Setup | Feature Setting | Sales | Contact Roles on Opportunities
Click the Gear Icon then go to Setup | Feature Setting | Service | Contact Roles on Cases

Note: "Contact Account Roles" are not available in the Lightning Interface.  See the Idea Exchange document below for reference.

Account Contact Roles in Lightning Experience

We have introduced a new feature,"Contacts to Multiple Accounts", that replaces the Account Contact Roles functionality plus more! 

Contacts to Multiple Accounts has all the capabilities that you have been asking for in Account Contact Roles including: 

• Custom field support
• Related list customization
• The ability to view the relationship from both the Account and Contact page layouts

Contacts to Multiple Accounts is available in Classic, Lightning and the Salesforce mobile app.

You can then:

• click "New" to add a new value

• click "Reorder" to reorder the values

• click "Replace" to globally replace an existing value in the picklist with a new value

• click "Edit" next to an existing value to edit the value's name and, optionally, make it the default value

• click "Del" next to an existing value to delete it and choose a replacement value to apply to records containing the deleted value.

The click path you choose will be determined by which object you would like the picklist value to be available for. For example, if you only need to add a value to Contact Roles for Accounts you would only need to follow the first click path and use the "New" button. If, however, you need to add a value and have it be available for Contact Roles related to all four objects you will need to follow each of the above click paths and add the value to each.