First time managing someone older than me - any tips?

Recently got promoted and now I’m managing someone who’s about 15 years older than me and has been in the company longer. They’ve been professional so far, but I can tell they’re not fully bought in yet. Nothing obvious, just small things like pushing back more than others or not really engaging in team discussions. I’m trying not to overcompensate or come off insecure, but I also don’t want to be too passive.

For those who’ve been in this situation, what actually helped you build that trust early on?