Tridacna clams are widespread throughout tropical regions and are important to several cultures as a food source and treasure, putting their populations under pressure. Within the Cook Islands there is a particular interest in understanding source-sink relationships among island populations of the small giant clam, Tridacna maxima, that could inform local conservation and management of stocks. In collaboration with the Ministry of Marine Resources, we investigated the genomic diversity and population connectivity of T. maxima using a Genotype-By-Sequencing approach to recover genome-wide, multilocus genotypes for individuals sampled across ten islands. Population genomic analysis revealed that the island population of Manihiki was most differentiated from the other sampled islands, and the island population of Palmerston Atoll likely provides a stepping-stone population between Manihiki and the southern island populations. The southern island populations were not greatly genetically differentiated and likely have regular, but in some cases asymmetric, gene flow among them. All the island populations had a heterozygote (genetic diversity) deficit, and high estimated values of inbreeding, although this was less the case for Manihiki and Palmerston Atoll. Such patterns of genetic diversity, and inbreeding values, may be indicative of small or reduced population sizes, owing to harvesting pressure.