The onset of the COVID-19 pandemic has brought the mental health of people under risk. Social counselling has gained remarkable significance in this environment. Unlike general goal-oriented dialogues, a conversation between a patient and a therapist is considerably implicit, though the objective of the conversation is quite apparent. In such a case, understanding the intent of the patient is imperative in providing effective counselling in therapy sessions, and the same applies to a dialogue system as well. In this work, we take forward a small but an important step in the development of an automated dialogue system for mental-health counselling. We develop a novel dataset, named HOPE, to provide a platform for the dialogue-act classification in counselling conversations. We identify the requirement of such conversation and propose twelve domain-specific dialogue-act (DAC) labels. We collect 12.9K utterances from publicly-available counselling session videos on YouTube, extract their transcripts, clean, and annotate them with DAC labels. Further, we propose SPARTA, a transformer-based architecture with a novel speaker- and time-aware contextual learning for the dialogue-act classification. Our evaluation shows convincing performance over several baselines, achieving state-of-the-art on HOPE. We also supplement our experiments with extensive empirical and qualitative analyses of SPARTA.