Multi-link operation (MLO) is a new and essential mechanism of IEEE 802.11be Extremely High Throughput (Wi-Fi 7) that can increase throughput and decrease latency in Wireless Local Area Networks (WLANs). The MLO enables a Multi-Link Device (MLD) to perform Simultaneous Transmission and Reception (STR) in different frequency bands. However, not all MLDs can support STR due to cross-link or in-device coexistence interference, while an STR-unable MLD (NSTR-MLD) can transmit multiple frames simultaneously in more than two links. This study focuses on the problems when NSTR-MLDs share a link with Single-Link Devices (SLDs). We propose a Contention-Less Synchronous Transmission (CLST) mechanism to improve fairness between NSTR-MLDs and SLDs while increasing the total network throughput. The proposed mechanism classifies links as MLD Dominant Links (MDLs) and Heterogeneous Coexistence Links (HCLs). In the proposed mechanism, an NSTR-MLD obtains a Synchronous Transmission Token (STT) through a virtual channel contention in the HCL but does not actually transmit a frame in the HCL, which is compensated for by a synchronous transmission triggered in the MDL. Moreover, the CLST mechanism allows additional subsequent transmissions up to the accumulated STT without further contention. Extensive simulation results confirm the outstanding performance of the CLST mechanism in terms of total throughput and fairness compared to existing synchronous transmission mechanisms.