What were the immediate consequences of the secession of South Carolina?

The secession of South Carolina from the United States in December 1860 was the result of a growing division between the North and the South. The northern states had all made slavery illegal, while in the South, rich landowners felt that the plantation economy and the importance of cotton production depended upon the continuance of the institution of slavery. In November 1860, the South Carolina General Assembly passed a resolution that the election of Abraham Lincoln as US President was a hostile act, and in late December 1860, the legislature announced:


We, therefore, the People of South Carolina, by our delegates in Convention assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, have solemnly declared that the Union heretofore existing between this State and the other States of North America, is dissolved, and that the State of South Carolina has resumed her position among the nations of the world, as a separate and independent State . . .


The immediate consequences of this act were swift steps leading to the outbreak of the Civil War. Within a few weeks of South Carolina's secession, Alabama, Georgia, Mississippi, Louisiana, Florida, and Texas had all left the Union. Delegates from these states met in Montgomery, Alabama and created a new government that they called the Confederate States of America. Jefferson Davis became the first president of the Confederacy.

A few days after the secession of South Carolina, Major Robert Anderson and a group of US soldiers took refuge in Fort Sumter in Charleston Harbor. After months of siege, Confederate troops bombarded the fort with heavy artillery beginning on April 12, 1861. In less than two days, Major Anderson was forced to surrender. The attack on Fort Sumter began the active fighting of the Civil War.
https://avalon.law.yale.edu/19th_century/csa_scarsec.asp

https://www.history.com/this-day-in-history/the-civil-war-begins

https://www.history.com/topics/american-civil-war/secession

The secession of South Carolina in December 1860 led to a wave of Southern patriotism. When then-president James Buchanan did not send troops into South Carolina to restore order, other states in the deep South formed their own secession conventions in order to separate from the United States. Before Lincoln's inauguration in March 1861, Florida, Texas, Louisiana, Georgia, Mississippi, and Alabama would all secede from the Union. While not everyone in these states favored creating a new nation, those that did were quite vocal in their desire. They created the notion that the Confederate states were on the same moral plane as the American colonies who had resisted British rule in 1776.
Also in this time following South Carolina's motion to secede, the newly minted Confederate states made plans to start seizing federal property within their respective states. This made garrisons in the states quite uneasy and at places like Fort Sumter and Fort Moultrie, they began to ask for more federal support and guidance.