I'm not 100% sure that I understand, but I think this satisfies what you're asking for. Note that this was assuming that the database is MySQL, you didn't specify. The syntax of the IF() and CONCAT() may be slightly different if it's something else.
EDIT: updated query as per Csharp's "answer" below. MAX
-ing the name is a bit of a hack.
SELECT t.TicketID,
MAX(CONCAT(p.FirstName, ' ', p.LastName)) AS RequesterFullName,
MAX(IF(a.Attribute = 'Urgent', a.AttributeValue, NULL)) AS UrgentPriorityID,
MAX(IF(a.Attribute = 'Medium', a.AttributeValue, NULL)) AS MediumPriorityID,
MAX(IF(a.Attribute = 'Low', a.AttributeValue, NULL)) AS LowPriorityID
FROM tblTicketIssues AS t
LEFT JOIN tblPersonnelProfile AS p ON p.PersonnelID = t.RequesterID
LEFT JOIN tblTicketAttribute AS a ON a.TicketID = t.TicketID
WHERE a.Attribute IN ('Urgent', 'Medium', 'Low')
GROUP BY t.TicketID;