Before you alter the outbound table map fields for Jira, you will need to add a new field in the table you will integrate. Doing so will sync your Jira Project field from Jira to ServiceNow's incident or change request table.
See Procedure
To get started with adding a Jira Project field to a table, follow these steps:
Navigate to the desired table
Log into ServiceNow and navigate to the Incident or Change Request table.
Create a Jira Project field
Configure the table and add a new field to the table. See Adding Fields to a Table in ServiceNow.
Select Choice in the Type field, and type Jira Projects as the Column label.
Check the Active box.
Then, click Advanced under the Related Links to access advance options.
Once the advance options are available, select PSP Utility as the Choice table and Jira Project as the Choice field.
Then, click Update.