The widespread use of surveillance cameras has initiated privacy concerns among individuals being captured by these devices. Due to the limited internal storage capacity, these cameras often transmit recorded videos over unreliable networks. This situation creates opportunities for attackers to exploit vulnerabilities, such as launching Man-in-the-Middle attacks, replayed scene attacks, and tampering with the video content. Considering these risks, this paper introduces a new chaotic map-based encryption scheme for surveillance videos. The work proposes a novel chaotic map using cascading and coupling operations on functions and is referred to as a Cascaded Coupled Logistic-Sine-Cosine (CCLSC) map. The chaotic performance of the novel CCLSC map has been evaluated using the Lyapunov exponent and the Bifurcation diagram. The scheme to encrypt surveillance videos is designed using the novel CCLSC map and our earlier designed Sine-Tangent-Sine (STS) chaotic map. The process involves extracting individual frames from the video and subsequently encrypts each frame as a digital image. The encryption of each frame involves three steps. The first step generates a Dynamic Chaotic Matrix (DCM) using CCLSC and STS map. The second phase is pixel scrambling using DCM and the final step changes the pixel values using DCM. Our results validate the security, robustness, and effectiveness of the proposed method.