EA Access is the console counterpart to the studio's Origin Access program on PC: a paid subscription service that lets you play any EA game in a growing collection, or jump into live games like Anthem earlier than everyone else. Currently, EA Access is only available on Xbox One - but it looks like its gearing up to make the jump to PS4.
Reddit user Sabazin uploaded a screengrab of the EA Access logo on the Brazilian PlayStation Store, with "já disponível" (which roughly translates to "available now") written underneath. Whether this is the result of a store bug, or someone unfortunately flipping a switch too early, that screengrab looks to be a pretty clear indication that EA Access is primed and ready for PS4.
Spanish site PureGaming did some further detective work, digging up references to PS4 and PlayStation Network accounts in the source code for the Brazilian EA Access purchase page. It makes sense that EA would want to include the PS4 player base in its pool of potential subscribers; at $5 a month or $30 for a full year, that's a lot of money EA is leaving on the table.
If you're thinking about signing up for EA Access if and when it arrives on PS4, the main things you need to know are: you can freely play any games in the EA Access library for as long as you're a subscriber, but it doesn't include free copies of EA's newest titles (unlike Microsoft's first-party approach to Xbox Game Pass). In other words, you currently can't jump into Anthem, Battlefield 5, or FIFA 19 straightaway with an EA Access subscription, but you can enjoy a sizable selection of EA games, including the entire Dragon Age and Mass Effect series.
If you want more PS4 freebies as part of a subscription, look no further than the free PS Plus games.