We sometimes have a use case for a custom field in which a user can add new values, but where already existing values would be presented as options. One way this could work would be to present already entered values in an autocomplete menu similar to the parent issue et al. autocomplete dropdown. This could be added as an option to text fields.

Another way that would be possible is with an additional option to the list or key/value custom field types where users could add new values to the list, with a mechanism similar to adding new categories or versions from the issue edit pane. I will open another ticket for this though.