Let’s understand this notion of a gap between the end of the Age of Grace and the resumption of the Age of Law is a purely human conjecture, unsupported by Scripture.
But once the rapture comes, the age of grace will officially end. Therefore, everyone saved after the rapture will be subject to the rules that will govern post-church salvation. I don’t believe God leaves cracks that people can unknowingly fall through into some kind of spiritual twilight zone.
The resumption of the Age of Law will primarily be obvious in Israel. That’s the only place there will be a temple with a priesthood conducting animal sacrifices. Gentiles around the world who become saved after the rapture will stay that way by obeying God’s commandments and remaining faithful to Jesus (Rev. 14:12).
Some people believe that with the rapture of the Church the Holy Spirit will disappear from Earth, but I don’t think that’s correct.
One of His responsibilities during the Church Age has been to act as a deposit guaranteeing our inheritance. Once the rapture occurs, the Gentiles will receive their inheritance, so it will no longer be necessary for Him to guarantee it. Keep in mind words by Paul saying we are sealed with Him unto the day of redemption (Ephes. 4:30).
After the rapture, He will stop restraining the secret power of lawlessness on earth. I believe at that time He will also resume a ministry similar to His Old Testament one, being with believers and coming upon them in power, but will not be sealed within them. He will guide these new believers into understanding what God requires of them just as He has always done.