LEOSA would be as useless as female secondary characteristics on a bowling ball if it did not trump general state law carry restrictions. It was amended a few years ago (mostly) to overcome the misconduct in NJ about their restrictions about hollow points in public. There are some residual restrictions, of course. One should read it themselves and have a very good knowledge of what it requires and what it will not overcome.
The best source I have found is Cornell Law:
18 U.S. Code SS 926B - Carrying of concealed firearms by qualified law enforcement officers | US Law | LII / Legal Information Institute for active, and
18 U.S. Code SS 926C - Carrying of concealed firearms by qualified retired law enforcement officers | US Law | LII / Legal Information Institute for retired. Among other issues, you need to know what counts as an LE Officer; what counts as active or retired, etc. You should also have at least some idea of the state laws wherever you are going (we are probably required to notify if carrying when stopped in those states where that exists; don't get stopped, dummy). For example, here in WA, out of state officers get the same exceptions in-state officers do, which are broader than LEOSA in most regards. (I can remember when the thankfully former Chief in Seattle had a kitten about LEOSA, not knowing that State law was broader and that the stupid local SPD policies were not even lawful as to their own personnel, let alone out of state cops, due to being inconsistent with the statute.)(I do LE legal at work, and some private research, writing and teaching on it - the blatant ignorance of most command officers and lawyers is truly shameful.)
Because of bad drafting, it probably does not provide an exception to the Gun Free Schools zone law (the federal one), as that requires that the person carrying have a license from whatever state you are in.