Is zakat obligatory on an apartment offered for sale, but which cannot be sold until an alternative dwelling is secured, knowing that its price is contingent upon settling a debt owed by the questioner's father?

There is no Zakat (definition) on real estate as long as the intention of trading was not present at the time of its acquisition, or if the intention to sell is not for trade but rather due to a desire to dispose of the property. Also, the majority of scholars hold that debt prevents the obligation of Zakat on hidden wealth.