All three sentences are grammatical:
After years of uncertainty and upheaval allowed ISIS militants to gain a foothold in the country, the U.S. has begun carrying out airstrikes to try and oust them.
After years of uncertainty and upheaval which allowed ISIS militants to gain a foothold in the country, the U.S. has begun carrying out airstrikes to try and oust them.
After years of uncertainty and upheaval that allowed ISIS militants to gain a foothold in the country, the U.S. has begun carrying out airstrikes to try and oust them.
After weeks of static and interference made him want to throw the damn phone against a brick wall, he decided to take it into the shop for repair.
After weeks of static and interference that made him want to throw the damn phone against a brick wall, he decided to take it into the shop for repair.
After weeks of static and interference which made him want to throw the damn phone against a brick wall, he decided to take it into the shop for repair.