Speaking to ESPN's Dave McMenamin, Davis said he would tell Williamson to "just go out there and play and have fun."
Davis can relate to what Williamson will experience as the designated franchise player and No. 1 overall draft pick as soon as he steps on the court.
"I for sure felt (the pressure)," Davis told McMenamin. "I just feel like if you're the first pick, it's like you have to win Rookie of the Year. I didn't, Dame [Lillard] did, but there's some type of pressure where you feel like you have to."
Davis began his career in New Orleans and made six straight All-Star teams from 2014-19 playing for the organization. He was traded to the Lakers in July after the Pelicans were able to draft Williamson.
Williamson sat out the first 44 games this season while recovering from October surgery to repair a torn meniscus. The 19-year-old's much-anticipated debut didn't disappoint. He scored 17 straight Pelicans points midway through the fourth quarter and finished with 22 on 8-of-11 shooting in 18 minutes.
Even though the San Antonio Spurs held on for a 121-117 win over the Pelicans, Williamson gave New Orleans a strong glimpse of what it can expect from him moving forward.