Does the Dutch Famine of 1944-45 count? It's the only example of a famine in a developed modern country and was caused by the effects of the Second World War.

Famines tend to be sparked by local food shortages but the real damage tends to come through interference with food distribution that prevents supplies reaching areas with local shortages. Nations with government systems based on popular representation don't tend to suffer from famine because they're disincentivised from simply leaving the market to work things out for itself as starving your voter base is counterproductive.

Things like the Great Irish Famine or the Indian famines under British rule occured because Irish and Indian subjects didn't have the representative clout to ensure that the colonial governments did something besides relying on market forces until the situation had already become grave.

Indian famines post independence (1960s Bihar and 1970s Maharashtra) are the answer to your question about famines in democracies.

These, however, were far less severe than the famines under colonial rule because of relatively quick deployment of aid.

Is there any particular reason you think there haven't? In antiquity famine was an ever-present threat for all societies, as prior to the Green Revolution even apparently minor shocks to agriculture could have wide-reaching, catastrophic effects. A single season's crop failure could and frequently did cause mass hunger, forcing cities and states to import food. Moreover in large cities, most famously Rome but also pretty much all others beyond a certain size, the local hinterland was routinely insufficient to feed the city, and food had to be imported, either bought or collected as tribute or tax. The Athenians survived mainly (exclusively, during the Spartan invasions of the Peloponnesian War) on grain from the Black Sea, and when this was disrupted, as was not uncommon, the city starved. If we consider Rome to be a democracy in the late Republic that city was constantly living at the edge of famine, and mass hunger broke out every few years. Famine struck ancient cities regardless of their government--what mattered was the ability of the economy to make up for agricultural losses by providing from elsewhere, and government had little to do with such things