God made a lot of promises, including being a heir. According to Merriam-Webster, a "heir" is basically "one who receives [...] from a parent or predecessor", and from the description a few verses earlier, all believers can be considered heirs. But the heir promise is something not by law but "through the righteousness of faith" (4:13).
In fact, Paul writes that "if those who are of the law are heirs, faith is made void" (4:14). In other words, those who obtain the heir through the law technically do not need faith to obtain the heir. But then again, that couldn't be done since we all have screwed up at least once (as seen in Romans 1-3).
In fact, Paul notes that "the law brings about wrath" and that "where there is no law there is no transgression" (4:15). Basically, part of the reason why we know we screwed up is because of the standards (whether the Mosaic Law or our own consciousness). These two basically reveal our need for a Savior (which Paul talked about in the latter part of Romans 3).