In that case stick to Imperial space and trade and / or do missions for the local allied forces. Always check the bulletin board for the rank up missions. I use to stay in one system and do as many missions an possible until I reach allied status with the locals. Then I switch to the next system. That way it does not take too long until you can progress to the next rank. And don't forget to ALWAYS check the bulletin board of Imperial stations for those rank up missions.