In Romans, you need Prestige to rank up your account and unlock access to higher-level research. To earn Prestige, one of the easiest ways is to upgrade and build more housing. Housing will passively generate Prestige for you at a pre-determined hourly rate. You can upgrade your housing to increase the speed and capacity that Prestige is generated. 

Alternatively, Prestige can be gained by defeating Barbarians or using an "Imperial Favour" card.

Once you have enough Prestige to rank up, your 'Player Info' Seal at the top right of the screen will start flashing green. Click on your seal to open the player info panel and from there you can rank up.