(1) Background This scoping review aimed to systematically map how non-technical care is conceptualised and practised within sport and exercise medicine (SEM), particularly in elite sport contexts. It explored perspectives of both SEM practitioners and athletes, focusing on relational attributes such as trust, communication, and practitioner characteristics that underpin non-technical care. (2) Methods: A scoping review was conducted following PRISMA-ScR guidelines and registered with the Open Science Framework. Three databases (PubMed, Sport Discus, ScienceDirect) were searched in August 2025, supplemented by hand searching. Eligibility criteria followed the PCC framework, including elite athletes and SEM practitioners, with a focus on non-technical care attributes. Twenty-three articles met the inclusion criteria. (3) Results Three overarching themes emerged: (1) Communication: Active listening, verbal/non-verbal strategies, and multidisciplinary dialogue; (2) Trust: Influenced by confidentiality, competence, and long-term relationships, though inconsistently defined; (3) Desired practitioner characteristics: Professional credibility, collaborative approaches, and personal attributes such as humility and empathy. Only one study referenced non-technical frameworks (therapeutic alliance and shared decision-making). (4) Conclusions: Non-technical care in SEM is primarily understood through trust and communication, yet lacks conceptual clarity and tailored frameworks. Findings highlight the need for models that integrate relational, ethical, and contextual dimensions of elite sport to support consistent, person-centred care.