Connecting desires for achievement, the satisfaction of basic psychological needs and the perception of fear of failure is one of the most relevant questions in the understanding of negative mental responses in youth athletes. How to act with less fear is what every athlete seeks to feel to enhance their performance actions. This paper aims to shed light on a sample of 681 members of sports teams belonging to different Spanish clubs (391 boys and 290 girls), with a mean age of 16.2 years, and a high sports dedication (75.5% > 5 years of experience; 96.3% > two training sessions/week; 90.3% > 3 hours of training/week). The collected data used self-reports based on the tenets of achievement motivation, Self-Determination Theory, and fear of failure. Those aspects linked to task involvement were positively close to Basic Psychological Needs (BPNs), while those related to ego involvement moved away from task involvement and BPNs. Fear was associated positively and significantly only with ego, and negatively with the rest of the constructs. In the standardized direct effect, positive and significant associations were observed among all constructs except between an ego-involving climate and basic psychological needs satisfaction. The association between a task-involving climate and BPNs was significant in fostering relationships among group members, as well as in improving interpersonal cohesion, empathic understanding processes, and reducing fear of failure in youth athletes.