You can listen to any issue event and call any REST service of your internal/external systems that you want to integrate with JIRA.

In the first step for define these listeners, you need to go (EI) Listeners page which defines in Easy Integration Menu.

 On this page, you can find your all listeners which you define before and you can do some operation with them. You can;

1. Create a new listener
2. Edit an existing listener
3. Delete an existing listener 

To create a new listener

1. Click Add New Listener button
2. Fill information about listener

1. Type your listener's name.
2. Select projects which you want to call rest in your system. Also, you can choose the All Projects option.
3. Select issue types which you want to call rest in your system. Also, you can choose the All  Issue Types option.
4. A select an issue event(s) which you want to call rest when will be. You can select more than one issue event.

Script for execution

In this section, you can give a decision to execute REST according to the result of the Groovy script.
By default, it has only return true statement. However, you can type your script and return true; to execute REST, or return false; not to execute

Below, there is a sample code on how you can type your own script.

import com.atlassian.jira.component.ComponentAccessor
import com.atlassian.jira.user.ApplicationUser

ApplicationUser currentUser = ComponentAccessor.getJiraAuthenticationContext().loggedInUser
log.info("current user:" + currentUser.username)
def reporter = issue.reporter.username
log.info("reporter: " + reporter)
return reporter.equals(currentUser.username)

REST Service Details

In this section, REST details (URL, method, headers, body, credential, ..) are filled.

1.  The endpoint of the REST service. You can type any dynamic parameter here using double curly braces. (e.g. http://mycompany.com/api/book/{{bookId}} assuming bookId is defined in Parameters section which is described below
2.  Select the Http Method (GET, POST, PUT, DELETE)
3. Define your HTTP header key/value sets in separate lines as described in screen-shot
4. Type JSON request body. You can use dynamic parameters here as well
5.  Define all your dynamic parameters here. You can add static values as well as the dynamic values of fields/custom fields in the JIRA issue. Here are some sample usages:
6.  Choose the authorization type. Currently, BASIC Authentication is supported.  If you choose Basic Authorization Type, credential becomes active, and the credentials you defined in the Credentials section are listed.

Headers code example;

Accept=application/json

Request body code example;

{
   "item"  : "{{productName}}",
   "price" : "{{price}}",
   "date"  : "{{date}}",
   "item"  : "{{productName}}",
   "owner" : "{{user.displayName}}"
}

Parameters code example;

assignee    = $issue.assignee or {{issue.assignee}}
reporter    = {{issue.reporter}}
date        = $issue.created
formattedDate = $DateTimeFormatter.ofPattern("yyyy-MM-dd HH:mm").format($issue.created)
productName = $issue.getCustomFieldValue($customFieldManager.getCustomFieldObject('customfield_11100'))
price       = $issue.getCustomFieldValue($customFieldManager.getCustomFieldObject('customfield_11102'))
displayName = $user.displayName
userDisplayName = $ComponentAccessor.getUserManager().getUserByName("someUser").getDisplayName() // you can also use ComponentAccessor
comment     = $comment // this is the comment that is passed through the transition

For more details and utils for parameter assigning see Parameters usage examples 
Also see ComponentAccessor, User, Issue and Status API for all properties and methods

Run asynchronously?

In this section, you can enable async to execute the REST service asynchronously. There are a couple of reasons why you may want to execute asynchronously.

1. Executing synchronously makes the user wait for the transition longer than usual. If the host of the REST service responds late or there is a connection time out between the JIRA server and the host, the users wait for the spinner a lot. So, it may be wise to enable async if your REST service responds slow

2. Some issue parameters may wait for calculation or reindexing. Some plugins may work background to populate the actual result of a custom field and you may want to use that value. 

There is a scheduled task named Easy Integrations for JIRA - Async Rest Caller Sched

Post operations

In this section, you can configure to update a custom field based on a value in the REST response

• First click on Update custom field checkbox
• Custom field drop-down is displayed, select the one you want to update
• Type jsonpath accordingly to select the value. If the result is not JSON and you want to update a custom field with the body itself, just leave this textbox empty.

1. Click the checkbox if you want to update any custom field
2. A select custom field which will be update
3. Type jsonpath for custom field

See jsonpath examples page for jsonpath samples.