Stole this from the SH3 Wiki:
"For your first promotion, you'll need to accumulate 5,000 renown. Your next promotion comes at 15,000 renown and the third promotion comes at 25,000 renown. The renown needed for a promotion is not the cumulative renown you've gathered through your career, but rather your current amount of renown.
The order of ranks are:
- Leutnant z. S.
- Oberleutnant z. S.
- Kapitänleutnant
- Korvettenkapitän
- Fregattenkapitän
- Kapitän z. S."