Agile methods have provided significant contributions to Software Engineering. This work presents a new process for Software Requirements Specification, integrating Agile Properties and regulated environments, such as aviation, medical, nuclear and automotive, among others. The Software in Regulated Environments (SRE) involves plan-driven methods with needed documentation to ensure safety, reliability, security, and discipline. This paper proposes a balance between agile and plan-driven methods. We define a new process, which explores and investigates the usage of agile methods in SRE. The scope of this paper is Requirements Engineering, which is considered as a set of activities involved in the management, elicitation, documentation, and maintenance of requirements. The Adile Requirements Specification (ARES) process contains four methods, 13 activities, and some required artifacts to ensure compliance with the following six relevant Software Standards for regulated environments: RTCA DO-178C, IEC 62304:2015, ECSS-E-ST-40C, IEC 61508-3, ISO/IEC/IEEE 12207, and IAEA SSG-39. The process evaluation was performed using two experiments: a Cockpit Display System (CDS) and a Healthcare Information System (HIS). These experiments were measured with appropriate metrics to ensure improvements in Software Requirements Specification and traceability among artifacts. The experimental results revealed that the ARES process works better than the original Scrum for Software in Regulated Environments. The ARES process can also be integrated with traditional software life cycles (Waterfall, V, and Incremental and Iterative), when applied in the Requirements Engineering phase.