It really isn't advisable to moderate system tables, in any way. Your trigger or any other addition could cause undesired behaviour and whenever a patch or service pack is applied to the SQL Server your modifications may disappear. Because of these reasons modifications to system owned objects are not allowed by default.
If you intend to create a trigger own your own table then you have defined a wrong table in the CREATE statement. Should it be something like:
CREATE TRIGGER TriggeredSuspect on MyTableNameGoesHere
INSTEAD of Update
AS declare @empname varchar(55), @empAdd varchar(55), @audit_action varchar(100);
select @empname='Suspect'
select @empAdd='Suspect'
set @audit_action='Inserted Record -- After Insert Trigger.';
insert into [TestDB].dbo.employee(emp_name,emp_add)
values (@empname,@empAdd);
PRINT 'AFTER INSERT trigger fired.'