Osama bin Laden’s death is a long-awaited day of justice for the American people and for all those innocents across the globe who suffered al-Qaeda’s brutality.

Some high-fives, sighs of relief, tears of closure and shout-outs of thanks to the pros — past and present — who have gone in harm’s way for our security are certainly in order. But this is no time for us to rest on our laurels.

While a very dark chapter in the War on Terror closed with Osama’s last breath and our minds flirt with dreams of peace, we still have big challenges ahead.

For instance, while the killing of the terror kingpin could signal the beginning of the end, al-Qaeda will likely try to find a new leader to promote and spread its bankrupt, violent ideology.

As such, the group will likely try to lash out to prove it’s viable after this huge loss in an effort to attract new foot soldiers, sympathizers and financial backers. Revenge will motivate, too.

Not to mention that some of al-Qaeda’s affiliates are already quite threatening. Al- Qaeda in the Arabian Peninsula (AQAP) is perhaps the most dangerous wing today.

In fact, Yemen-based AQAP is responsible for at least three plots against the United States in just the last 18 months: the Fort Hood shootings, the Detroit underwear bomber and the ink-cartridge caper.

Of course, there’s also the matter of Afghanistan, where some 100,000 U.S. troops are facing the terrorist Taliban, which just announced its spring offensive.

The Taliban provided al-Qaeda safe haven prior to 9/11. It may be willing to do the same again if the Taliban prevails in Afghanistan, meaning more terror trouble.

And what of Pakistan, which some see as “terror central?” Hard to know, but we’ve seen plots directed our way from there before — and it’s troubling that Osama was living not far from Islamabad.

While Osama bin Laden’s demise is a victory we should relish, we still face a longer war against violent extremism. Embracing complacency about the threat comes only at our peril. Unfortunately, there’s still work to be done.

Peter Brookes is a Heritage Foundation senior fellow and a former deputy assistant secretary of defense.