Trading bitcoin (and people accumulating it) takes place on the market and is unrelated to mining and its reward. People buy and sell bitcoin from and to each other on the market. Any coin you buy from an exchange today is many "hops" from a coinbase reward. Which means in the future without a block reward, the market should not change at all. People will still continue trading with each other with the coins they have.
The only thing that changes is when "supply" of fresh coins entering the market/circulation decreases while "demand" goes up, the price should go higher. Which is one of the reasons why we usually have a big bull market each 4 years starting after the halving (supply cut by 50%).
Unlike fiat currency Bitcoin has limited supply that is rolling out in controlled manner. With time more and more people and organizations are getting familiar with Bitcoin and they are buying Bitcoins to book their future profit, that's where bitcoin "Demand and supply" plays a key role in increasing its price. It's also a fact that bitcoin has total supply of 21 million coins and a good amount of bitcoins are already lost because of different reasons and its assumed that they won't be ever recover.