SQL best way I can think of is add it like this:
IF NOT EXISTS (
select 1 FROM APP_PROJECT_GROUP WHERE GROUP_NAME = :v_group_name AND USER_ID = :v_user_id
)
BEGIN
INSERT INTO APP_PROJECT_GROUP (GROUP_ID, GROUP_NAME, PROJECT_ID, USER_ID) VALUES (v_group_id, v_group_name, v_project_id, v_user_i)
END
END