Yes, after completion of LLB, one can further pursue LLM. The LLM is a postgraduate degree in law, which provides a specialism for graduates in such areas as international law, corporate law, human rights, criminal law, or intellectual property. It is especially for those wishing to extend their legal knowledge, engage in research, or advance their professional qualifications.
An LLM can also lead to teaching posts in law schools, legal consultancy, or higher ranking at law firms and corporations. It is also another important qualification in a career that leads to legal writing, making policies, or international organizations. Generally, the LL.M takes a year full time and two years for part timers. There are a lot of LLM programs offered in various universities worldwide, some of which are noted for putting special emphasis on particular fields of law. This is often particularly more advantageous if you're planning to venture into an academic or research career in law.