The new tax regime (NTR) was introduced by the Finance Act 2020. At that time, NTR was an optional regime while the old tax regime (OTR) remained the default regime. 

Under the NTR, certain specified exemptions or deductions towards HRA, Leave Travel Allowance (LTA), set-off of loss from house property, Chapter VIA deductions (80C, 80D etc.), among others, are not available.

Even if the employer has applied the default NTR while computing taxes on salary and, hence, not provided the deductions, a salaried taxpayer may still choose to opt out of the default NTR and apply the OTR, while filing the annual income-tax return, provided the return is filed within the applicable statutory due date of filing of original tax return (31 July 2024) for FY24 in the case of salaried taxpayers not subject to tax audit. 

In case the same applies to you, it should be within the tax provisions, and you may wait for the processing of your tax return.

Having said this, since Form 16 is issued by the employer under NTR and return of income is filed by you under OTR claiming additional deductions or exemptions, it is important that you have the documentary evidence in support of such deductions and exemptions being claimed in the income-tax return, in case of any assessment or enquiry from the income-tax department at a future date.