I assume that you are defining the “newly born democracy in South Africa” as the one that arose after the end of apartheid in 1994. If so, we can probably argue that it is better to say that South Africa needed a *new* constitution, not just that it needed a constitution.
All democracies need a constitution in order to be truly democratic. They need this because democracy depends in part on the rule of law. There need to be laws that are set out to determine how the country’s government will be set up, what powers it will have, and what rights its citizens will have. For this reason, South Africa needed a constitution.
However, South Africa already had a constitution and so what it needed was a new constitution. It needed a new constitution because its previous constitution had been based on the racist principles that were behind the apartheid regime. The previous constitution, for example, had provided no representation for Blacks in the Tricameral Parliament. In 1994, South Africa threw off apartheid and began to remake itself as a truly democratic country with majority rule. In order to do this, it needed a new constitution. It needed a new constitution that would be different from the old, racist constitution. It had to have a new constitution to erase the racism that pervaded the old.
When a democracy is going to make fundamental changes in its nature, it needs a new constitution. South Africa had been a democracy, but only for its white citizens. To become a true, majoritarian democracy, it had to have a new constitution that would embody its new values.