Answer: There is no restriction on you claiming HRA while claiming tax benefits in respect of home loan as long as you are satisfying the conditions laid down under Section 10 (13A) and 80C and 24(b). Since you are paying rent for the house in which you are staying and which is not owned by you, you can claim the HRA benefit.
As you are planning to let out the property and in case you are able to do so before 31st March, you can show this property as let out and claim the tax benefits in respect of interest paid under Section 24(b) and for repayment of home loan under Section 80 C up to Rs. 1.50 lakh along with other eligible items. The tax benefits for home loan are available for the full year in which possession of the property is taken. So you will be able to claim the benefits of HRA and home loan for the full year as you intend to stay in the rented house for the whole year.
The income tax laws allow a person to have maximum of two houses as self-occupied so even if you are not able to let out your house before 31st March, you can show it as self-occupied and I do not think there should be any problem as long as this house is not actually let out during the year. Once you start letting out the house, you can claim vacancy allowance for the period during the year when it cannot actually be let out.
Source: https://www.livemint.com/budget/news/claiming-hra-and-home-loan-income-tax-benefits-simultaneously-explained-11643598573263.html
There is no restriction on you claiming HRA while claiming tax benefits in respect of home loan, provided some conditions are satisfied