Can I use Liepard's "Trade" Ability if there are no cards in my deck, just to discard a card?
No, you can't use Trade if there aren't any cards left in your deck. Discarding a card from your hand is a cost to use the Ability, and drawing cards is the effect.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_91
SWSH9_91