Aside from character creation, the occasional boosts you get from certain choices/relationships you can raise leadership in your free time by exploring the kitchens <3

Here's a couple other ways: 

1. Clarmont's week 1 date will give you +10 leadership as long as you don't mess it up

2. In Penelope's week 2 friendship date, if you're friends with both her and Lisle, then Lisle will pop in for a visit. You'll get +5 charm from Pen and +5 leadership from Lisle.

3. In week 2, visit the garden during your free time. If you have high enough romance with Clarmont, he'll be there. You two will take a walk through the gardens and you'll get +5 leadership.