Compare e obtenha os novos dados inseridos na tabela com base no mês

você poderia usar um menos

select SYS_DB_NAME, ENTITY_ID, MONTH_ID
from my_table 
where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( extract(month from sysdate), 2,'0')
minus  
select  SYS_DB_NAME, ENTITY_ID, MONTH_ID
from my_table 
where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( (extract(month from sysdate) -1) , 2,'0')

e se você precisar do conteúdo das linhas

select * from  my_table  m
inner join  (
    select SYS_DB_NAME, ENTITY_ID, MONTH_ID
    from my_table 
    where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( extract(month from sysdate), 2,'0')
    minus  
    select  SYS_DB_NAME, ENTITY_ID, MONTH_ID
    from my_table 
    where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( (extract(month from sysdate) -1) , 2,'0')
) T on m.SYS_DB_NAME = t.SYS_DB_NAME 
      AND m.ENTITY_ID = t.ENTITY_ID 
        AND m.MONTH_ID = t.MONTH_ID

e se você precisa apenas contar

select count(*) from  
inner join  (
    select SYS_DB_NAME, ENTITY_ID, MONTH_ID
    from my_table 
    where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( extract(month from sysdate), 2,'0')
    minus  
    select  SYS_DB_NAME, ENTITY_ID, MONTH_ID
    from my_table 
    where MONTH_ID = to_char(sysdate, 'YYYY') || lpad( (extract(month from sysdate) -1) , 2,'0')
) T