A.T. Robertson Commentary 1 Timothy 5:20

"Them that sin reprove in the sight of all, that the rest also may be in fear." — 1 Timothy 5:20 (ASV)

Them that sin (τους αμαρτανοντας). The elders who continue to sin (present active participle).

In the sight of all (ενωπιον παντων). "In the eye of (ο εν οπ ων, the one who is in the eye of, then combined = ενωπιον) all" the elders (or even of the church). See next verse 21 and Ga 1:20. Public rebuke when a clear case, not promiscuous gossip.

May be in fear (φοβον εχωσιν). Present active subjunctive with ινα (final clause), "may keep on having fear" (of exposure). Possibly, "the rest of the elders."