This guide will teach you how to make a difference between new tickets and ongoing discussions. There are two ways.
Saved queries
Firstly you have to create the needed Issue statuses in Administration - Issues statuses.
In our situation, the New status is important because all newly arrived tickets will be assigned to it. And In progress is the other important as it includes all the ongoing discussions. This could be set in the project helpdesk settings.
Then, please go to the Tickets list and set the filter of the Issue status to be In progress. Afterward, save the query.
The saved query could be accessed anytime by the support agents on the right-side panel.
The situation with the New tickets is identical.
And then the saved query that is available for the support agents would look like this.
Automation rules
If you do not like the above way with Issue statuses, then you could use an alternative one via the automation rules and Priority feature.
Please go to Administration - Helpdesk - Email rules. Here you have to create 2 rules. The first one should look like as below.
This rule means that for all incoming messages when they are New (i.e. the very first message that arrives at the support email), the Priority is automatically set as Immediately.
Note: Please keep in mind in the replies exchanging (the ticket discussion afterward), the above rule will be not applied as it is valid only for the very first message and not for the replies from the client (end-user) from now on.
And the second rule should be this one.
It means that for all Outgoing messages (i.e. answers of the support agent that are going to be sent to the end-users/clients), the Priority is automatically set to be Normal.
So, all New tickets will be bold and colored with red (as they are "Immediate priority") and all Replies from clients to existing discussions will be in normal font and non-red because they are "Normal priority". Please check the screenshot below to see it illustrated in the full list of all tickets (both replies and new messages in the list).