I had to update the app manually to make it appear. You need trade tokens to be able to trade 3-diamond or higher cards. You can get tokens by consuming cards, similar to how to get flair:

• Consuming a 3-diamond card gets you 25 trade tokens
• An ex card gets you 125 tokens.
• A 1-star card gets you 100 tokens.
• A 2-star or 3-star gets you 300 tokens (both of these are a terrible deal imo).

So in order to trade a single 3-diamond card, you first need to consume five others. Similarly for ex and 1-stars, you first need to consume four others, respectively.