Players picked at #13 in recent drafts:
2023: Zachary Benson (BUF)
2022: Frank Nazar (CHI)
2021: Matt Coronato (CGY)
2020: Seth Jarvis (CAR)
2019: Spencer Knight (FLA)
2018: Ty Dellandrea (DAL)
2017: Nick Suzuki (VGK)
2016: Jake Bean (CAR)
2015: Jakub Zboril (BOS)
2014: Jakub Vrana (WAS)
2013: Josh Morrissey (WPG)
2012: Radek Faksa (DAL)
2011: Sven Baertschi (CAL)
2010: Brandon Gormley (PHO)
2009: Zach Kassian (BUF)
And in 2016, 1 pick later, Charlie McAvoy.
In 2015, 3 picks later, the run of Barzal, Connor, Chabot
In 2014, 2 picks later, Dylan Larkin
In 2012, 4 picks later, Tomas Hertl
In 2011, 2 picks later, JT Miller