You need to collect character shards to recruit and ultimately increase the Star Rank of your characters. Character shards are dropped in Campaign missions, collected by opening orbs, earned in events or Challenges, or purchased in the Store.
One great way to find character shards is by going to the roster menu, tap on any character, tap "find" button, and this will give you places in the game where you can potentially obtain that specific characters shards.
Tip: Collecting more shards of a character allows you to increase the Star Rank. This not only boosts the character's Power but will also unlock character-specific and Star Rank-restricted events or missions.