For example, someone decides to go vegan but already owns a leather jacket?
What should they do with this jacket and any other non-vegan possessions?
Ask yourself, in the end it is you who decides.
Keeping the old non-vegan stuff but not getting any new; you find it ethical and sound to keep wearing your leather jacket because you are honoring the donor, so to speak. You would feel guilty to throw it away rather than keep using it till the end.
Giving it away instead; you find it abhorring to keep using that leather jacket, but you have no heart to throw it away. Letting someone else use it is totally fine with you though.
Throwing it away; you absolutely cannot see yourself or someone else use that leather jacket. You have to throw it away. Perhaps you feel a need for some last rites to be perxormed?
Again, ask yourself. It is only you who knows your own mind and heart.