Adam Clarke on Acts 4:17

But that it spread no farther - Not the news of the miraculous healing of the lame man, but the doctrine and influence which these men preach and exert. More than a thousand people had already professed faith in Christ in consequence of this miracle, (see Act 4:4), and if this teaching should be permitted to go on, probably accompanied with similar miracles, they had reason to believe that all Jerusalem (themselves excepted, who had steeled their hearts against all good) should be converted to the religion of him whom they had lately crucified.

Let us straitly threaten them - Απειλῃ απειλησωμεθα, Let us threaten them with threatening, a Hebraism, and a proof that St. Luke has translated the words of the council into Greek, just as they were spoken.

That they speak ...to no man in this name - Nothing so ominous to them as the name of Christ crucified, because they themselves had been his crucifiers. On this account they could not bear to hear salvation preached to mankind through him of whom they had been the betrayers and murderers, and who was soon likely to have no enemies but themselves.