Not much of what the prophets said was predictive; it was usually ethical. However, there is the intriguing overlap of this mentioned in the lines of Acts 3 (Dt 18) about the prophet like (Moses) who was coming. That is a predictive and ethic-driven One was on its way. The prediction is that anyone (in Israel) who does not listen to his appeal would be disinherited. The appeal? To join in the mission work to the nations, the blessing to all peoples on earth.
That mission work, as you put it, is after this...
Matthew 10:23 But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.
...which is what this was referring to...
Acts 3:19 Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord; 3:20 And he shall send Jesus Christ, which before was preached unto you: 3:21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
See this here...
Luke 24:46 And said unto them, Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day: 24:47 And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.
That is completed after Matt. 10:23.
Which is this here...
Isaiah 60:1 Arise, shine; for thy light is come, and the glory of the LORD is risen upon thee. 60:2 For, behold, the darkness shall cover the earth, and gross darkness the people: but the LORD shall arise upon thee, and his glory shall be seen upon thee. 60:3 And the Gentiles shall come to thy light, and kings to the brightness of thy rising.
Said gross darkness prior to all that being this here...
Acts 2:19 And I will shew wonders in heaven above, and signs in the earth beneath; blood, and fire, and vapour of smoke: 2:20 The sun shall be turned into darkness, and the moon into blood, before that great and notable day of the Lord come: 2:21 And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved.
Acts 3:22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you. 3:23 And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people.
So what happened that a large part of that did not play out to its prophesied end?
Making it something else is no answer.
Neither is reading Acts 13 into it as some kind of a continuance and or replacement.