I'm assuming your running stock. First, some recruits (higher ranks)cost renown and they must be dragged into empty spaces. (while in port) The low skill swabbies at the bottom of the list are free and they are the only ones you can choose if you have your allotted number of officers onboard.
The game will not let you add more officers than allowed and to get the option to promote your current people, you have to dismiss some of them. Once you cut some of your (say petty officers) loose, you will find promotions available. Keep in mind in real life, you lost about 1/3 of your crew each patrol.
If your using RFB, things are a bit different. LukeFF and the RFB team did a lot of work with crew management.
