Is it permissible to repay a debt, incurred for a business project, from the profits of that project?

If you borrow money from your relative to use as capital for a business venture between you, there is no harm in that.

However, stipulating that the loan be repaid only from the profits is impermissible due to jahalah (uncertainty) and gharar (risk/deception). But if the intention is to repay from the profits if they exist, and otherwise from your own money, then there is no harm.

Not setting a due date for the repayment of the debt does not cause harm according to some scholars.