First, personally if this is auditing I would add a row whenever a modification is done including necessary timestamps.
But to your question, you can also use MERGE for the upsert. For example something like:
MERGE tbl_Audit_Master AS target
USING (SELECT i.Emp_ID, i.Emp_Name, i.Designation
from inserted i, tbl_Audit_Master tam
where
) AS source (Emp_ID, Emp_Name, Designation)
ON (target.emp_id = source.emp_id
and target.emp_name = source.emp_name
and target.designation = source.designation)
WHEN NOT MATCHED BY TARGET THEN
INSERT (Emp_ID, Emp_Name, Designation)
VALUES (Emp_ID, Emp_Name, Designation);
GO