
He can be summoned in the Consumed King's Garden for Oceiros, the Consumed King. If you don't pick up his shield from Andre, you can still find it in front of the grave Hawkwood used to visit.
Once all 3 of the aforementioned bosses are all dead, Hawkwood will leave Firelink Shrine after a time, leaving his shield with Andre as a gift to you. After killing the Abyss Watchers, speak with Hawkwood and he gives you the Farron Ring. If you don't get anything, come back after Crystal Sage. Speak to Hawkwood after killing the Curse-Rotted Greatwood to receive a Heavy Gem. Speak to Hawkwood at the beginning of the game and you will receive the Collapse gesture. At times he wonders off to kneel in front of a gravestone near the shrine, but otherwise he doesn't move much. He likes to sit on the right landing leading down to the bonfire in Firelink Shrine. Hawkwood is likely the first NPC you will meet in Dark Souls 3.
You could always skim over our Beginner's Guide if you're having trouble getting started.
If you haven't finished the game yet, bookmark this page for later and turn back. I'm sure you've guessed it, but there are spoilers ahead. Looking for NPCs like Greirat, Irina, or Yoel? Check out the Complete Guide to Firelink Shrine.