Reading Events - Reading events appear in your Inbox tab and you can complete them for ink. They usually reward around 300 to 500 ink, depending on the series and the required number of episodes read. These reading events are typically held the day or two after a series is released

Daily Ink Bonuses - Tapas sometimes gives out free ink during their events or holiday such as Christmas. Right now, tapas is giving out 500 ink daily

Fortune Cookie Mondays - Every monday, you can open a fortune cookie in your inbox.  On average, it'll give you 300-500 ink

Miscellaneous Challenges - Tapas also holds occasional events for free ink such as Treasure Hunts, Milestones, and more