Hi
Not sure how you want to remove the search field but you will need to modify code to do that. The file you need to modify is components/com_helpdeskpro/View/Tickets/tmpl/default.php
Once the modification is done, please move the modified file to templates/template_name/html/com_helpdeskpro/Tickets folder so that the change won't be lost when you update to future releases of the extension
Regards,
Tuan