You need to find an Imperial Navy Mission to complete for the next rank. If you flip the boards enough you can usually find a pretty easy transport mission rather than the dumb "KILL xxx number of ships" type.
Long system spec sig follows:
PowerSpec G436 Lian Li ATX 205 MSI Z490 Plus Motherboard Intel Core i7 10700K 3.8 GHz 32 GB RAM DDR4 1600 Nvidia RTX3070