Getting promoted depends on your renown level and how you spend your renown. In real life, back then, to get promoted depended on many factors, your tonnage numbers, your loyalty to the Fuher, your education, your skills, your leadership skills, pretty much it stayed the same as how u get promoted today.
Here Our the officer ranks that you can get in SH3
SEEKADETT
FÄHNRICH Z. S.
OBERFÄHNRICH Z. S.
LEUTNANT Z. S.
OBERLEUTNANT Z. S.
KAPITÄNLEUTNANT
KORVETTENKAPITÄN
FREGATTENKAPITÄN
Here is a link to a site that has the German, British and American Ranks http://jtmcdaniel.com/rank.html
FREGATTENKAPITÄN is the highest rank a player can achieve in the game and thats if you "edit" some files,,, which i did. If you held the same rank in the US Navy you would be Commander, below Captain. I wish that when you "retired" with SH3 Commander they would promote you to Kapitan zur See, a Full Captain and if you wanted to come out of retirement they would dropp you down to FREGATTENKAPITÄN. Just saying, hahaha. I also wish that the other officers in ur boat could be promoted higher too.
The thing with "editing" your rank to FREGATTENKAPITÄN is that you must have the reguired renown to do it otherwise SH3 Commander would dropp you down. I forget which file or files you need to mod but someone know the answer.