Does the tax saved after switching the regime get's reflected in current FY ?

I work in 1 company in Bangalore , Between 1-10th April in there portal option was provided to choose between old regime and new regime . I selected new regime , and i noticed in there's a lot of tax deduction in new regime . Later on i took help of my CA and got to know that if we consider HRA also so i am getting benefitted in old regime . 

Now i want to switch to old regime , i know that we can change while filing ITR , What i want to know is , if i change to old regime while filing ITR , would i get the upcoming month's salary(AUG2023 -MARCH 2024) considering old regime tax deductions ultimately increase in inhand salary ?