Geography Lesson

Can an extinct volcano become active again?

How are volcanoes formed?

Volcanoes are formed when magma from within the Earth's upper mantle pulls its way to the surface. At the surface, it emits to form lava streams and ash deposits. 

What is an extinct volcano?

An extinct volcano is one that no longer has a source of magma underneath it, and therefore has no way to erupt. This means they aren't expected to erupt again.

What causes a volcano to go extinct?
An extinct volcano happens when they’re cut off from their quantity of lava. This is where a chamber of magma beneath the surface of the Earth finds its way to the surface through weaknesses in the crust. 

....But the main question is 'Can an extinct volcano become active again?'. 
Well after doing some research an extinct volcano by definition is a dead volcano, which has not vented in the last 10,000 years and is not presumed to ever erupt again. In other words, the terminology extinct volcano indicates that there is no magmatic motion going on in the volcano. But according to Live Science a volcano just outside of Rome, long thought extinct, is rumbling to life. Colli Albani is a volcanic cluster of hills located 30 kilometres from the centre of Rome. Records show that there were no activities of an eruption, therefore it was given the thought of extinction. A team of researches from the American Geophysical Union found that the ground beneath the volcano is rising at a maximum of about 2 millimetres per year in areas where stem vents are merging. Colli Albani is arguably overdue for an eruption, but the volcano won't unexpectedly blow its top, Even then, Romans can expect plenty of warning, as an explosive eruption would be preceded by initial stages of moderate volcanic activity.

So to conclude this research, I think that yes extinct volcanoes can become active again but not all. Take Colli Albani as an example.

Resources: 
https://www.livescience.com/55397-extinct-Rome-volcano-rumbles-to-life.html