First, there is something wrong with this question. There are not high barriers to entry in a market that is in perfect competition. In fact, there are essentially no barriers. There are high barriers to entry in an oligopoly and insurmountable barriers in a monopoly, but this is not the case in perfect competition. I will assume that the question refers to perfect competition and that “high barriers” is a mistake.
In perfect competition, there are essentially no barriers to entry into the market. Anyone who wants to start producing that good or service can do so. This makes it so that there can be no possibility of economic profit in such a market. There can be stages in a perfectly competitive market in which there are not yet enough producers in that market. The producers who are in can be making positive economic profit. That will, however, inspire more companies to enter the market to compete. Because there are no barriers to entry, they all enter the market. This increases the supply of the product, causing prices to drop. When prices drop, economic profit is no longer possible.
Thus, in the long term, economic profit is not possible in perfect competition because there are essentially no barriers to entry.