I like this passage from Matthew McDill’s dissertation “The Authority of Church Elders in this New Testament” where he discusses the meaning of the phrase “keeping watch over your souls” from Hebrews 13:17:
Not only is this the reason given for the believers to submit to them, it describes the sphere in which they provided leadership (cf. 1 Thess 5:12, â€œthose who lead you in the Lordâ€). Several helpful parallels may be observed in Acts 20:28â€“32 and 1 Pet 5:1â€“4. The elders in Acts and 1 Peter are responsible for caring for (Ï€Î¿Î¹Î¼Î±Î¯Î½Ï‰) and watching over (á¼Ï€Î¯ÏƒÎºÎ¿Ï€Î¿Ï‚, á¼Ï€Î¹ÏƒÎºÎ¿Ï€ÎÏ‰) Godâ€™s people. Jesus is the shepherd (Ï€Î¿Î¹Î¼Î·ÌÎ½) and overseer (á¼Ï€Î¯ÏƒÎºÎ¿Ï€Î¿Ï‚) â€œof your soulsâ€ (Ï„á¿¶Î½ ÏˆÏ…Ï‡á¿¶Î½ á½‘Î¼á¿¶Î½) (1 Pet 2:25) and is the chief shepherd who will appear and reward the elders for their shepherding (1 Pet 5:4). Believers were entrusted into the care (ÎºÎ»á¿†ÏÎ¿Ï‚) of the elders (1 Pet 5:3). Caring for the church is not merely a charismatic function but is the specific responsibility and purpose of the Spiritâ€™s appointment (Acts 20:28). That this is an assigned responsibility is also confirmed by the requirement to give an account (Heb 13:17; 1 Pet 5:4).
So, if I understand Matthew, then he is saying that the phrase “keeping watch over your souls” is simply another way of saying “shepherding” or “caring for.”
It’s interesting that the author of Hebrews doesn’t mention “elders.” Perhaps all leaders, and even all believers, were to care for one another?