Construction of another house property may start before the sale of the house property in question, but it should be completed within the specified time of claiming exemption u/s 54F. For your clarity, I am stating the law in a bit simplified form. For bare text, kindly refer https://www.incometaxindia.gov.in/pages/acts/income-tax-act.aspx
U/s 54F, any long term capital gains arising to any individual of HUF from sale of residential house property(whether self occupied or on rent), shall be exempt to the extent such capital gain is invested in:
- Purchase of another Residential House property within one year before or two years after the due date of transfer of the property sold and/or;
- Construction of residential house property within a period of 3 years from the date of acquisition.
The New House Property must be held as capital asset for 3 years from the date of purchase or construction.
Relevant case laws- CIT vs Bharti Mishra, UOI vs Wood Papers Limited, G.P. Ceramics Pvt Ltd. vs CTT