There is an ever-increasing demand for Higher Education Institutions (HEIs) to engage with the challenges of the changing labour market contexts and trends, such as the Fifth Industrial Revolution and the new normal. However, a major criticism is that higher education institutions do not often prepare graduates for real-life contexts. For that reason, it is not surprising that graduate employability and the competencies required have become the primary concerns of HEIs. Often, we see the phrases "competency" and "employability" presented in the literature as essential requirements for graduates to attain gainful employment streams. Some studies also present them as interrelated concepts. However, we seldom find studies that unravel their intertwined relationships. This article tries to bridge this gap by looking into the role of HEIs in promoting the development of competencies for employability. We used a structured questionnaire to collect the quantitative data from 389 postgraduate students enrolled in a generic stream from an Indian State, Kerala. This paper proposes and tests a structural model of relationships between the perceived competencies of the postgraduates and their perceived career preparedness and, subsequently, perceived employability. This paper also highlights the need to reimagine tertiary education to suit the demands of changing times.