Police have stepped up anti-drug operataions in Discovery Bay following reports of drug-taking and under age drinking among expatriate teenagers in the Lantau enclave.这里的follow 为什么使用-ing形式呢？1.

你把这句话的顺序这样颠倒一下就明白了：

Following reports of drug-taking and under age drinking among expatriate teenagers in the Lantau enclave，Police have stepped up anti-drug operataions in Discovery Bay.

这句话抽象为：

Following…… ，+完整句子。following做状语。

或者，你也可以这样看： 完整句子+following……=完整句子，which follows……。把它看作一个 由定语从句演变而来的 非谓语动词（follow-ing）作定语 结构

following  状语从句。