In a video interview with Variety, Woody Harrelson seemed to confirm the role he is playing in the young Han Solo movie. When directly asked if he would be playing Garris Shrike, the actor answered with a simple "yes". The character was first created for the Expanded Universe (EU) back in 1997 in a series of books about the life of Han Solo. The EU was once canonical collection of books, video games, comic book stories about the larger Star Wars universe before Disney made the decision that is was no longer part of canon and no one is allowed to create new stories for this "Legends" take of Star Wars out of fear of confusing new Star Wars fans.
However, the EU is chock full of already vetted intellectual property so it makes sense to mine it for characters that they can introduce (while throwing the occasional bone to EU fans) as new all over again. In that alternate take, Shrike was the man that raised, abused, and trained Han Solo to become the smuggler we all know and love. In the movie we know he is Solo's mentor but to early to say if that extends to father figure. If you are interested in the characters full back story, head over to Wookieepedia. To help with the time line notes, remember that BYY means "Before the Battle of Yavin" as depicted in Star Wars: A New Hope. The destruction of the first Death Star acts as a marker of Year 0 on the Star Wars time line. Thanks to Feris O. for the link.