I think there is an easier solution than to create a new tab/section on a form and populate a field on there with the results of your filter condition. Would creating a custom related list between the u_apm_software and cmdb_ci_server tables, applying a default dynamic filter on the related list (server name starts with app name) and modifying the list_edit ACL for the related list so that it is read only for all satisfy the requirements? If yes, use these 2 links for how-to 

https://www.servicenow.com/community/developer-articles/servicenow-create-custom-related-list-servic...

https://www.servicenow.com/community/itsm-forum/making-a-related-list-read-only-for-a-specific-role/...

Please also consider the following - the request itself seems routed in a customization ex/ u_apm_software table? Out of the box, you can use the Business App table (cmdb_ci_business_app). Following the CSDM relationships, Business Apps consume App Services, and App Services Depend on Infrastructure (like servers). Build the appropriate Service Maps using the prescribed CSDM relationships and you can view the related servers by filtering on relationship level and/or type.