Cooperative Intelligent Transport Systems (C-ITS) Deployment Platform is considered the newest version of vehicular communication systems, which enables the cooperation between two or more ITS sub-systems to provide enhanced services. With the expanded communication range and system complexity, ensuring the credibility of access nodes and protecting users from being monitored has become a difficult problem in network security, especially the services provided by remote servers like navigation. Transport Layer Security (TLS) is widely used for user authentication and encrypted data transmission in all networks. However, although the TLS handshake complexity is significantly reduced in TLS 1.3 the transmission of a full certificate chain during the handshake is still costly, especially for high-mobility vehicles. In this paper, we propose an optional extension named Certificate Get to reduce the TLS handshake overhead in C-ITS. Specifically, with our proposed extension, the revisiting client transmits a hash value of the certificate chain corresponding to a certain server in the ClientHello message, which can reduce the transmission payload of the certificate chain from an average of 4874 bytes to 68 bytes. Simulation results show that our proposed scheme achieves a significant performance gain by greatly reducing the certificate transmission delay by 50% for both TLS 1.3 and TLS 1.2.