Your last paragraph is about clergy but about submitting to the rulers in each town/region, etc. These are not clergy, they are rulers.
False; those rulers are spiritual rulers. They were introduced ten verses previously (I will repost both references to rulers in Hebrews, followed up with passages written to Timothy, of whom the Apostle Paul was spiritual father, and appointed a bishop). The Apostle reinforces the lesson that those who submit and obey Bishop Timothy will profit thereby, where Timothy will save both himself and those who hear him.
Remember them which have the rule over you, who have spoken unto you the word of God: whose faith follow, considering the end of their conversation.
Obey them that have the rule over you, and submit yourselves: for they watch for your souls, as they that must give account, that they may do it with joy, and not with grief: for that is unprofitable for you.
Hebrews, Catholic chapter thirteen, Protestant verse seven,
Hebrews, Catholic chapter thirteen, Protestant verse seventeen,
as authorized, but not authored, by King James
And I thank Christ Jesus our Lord, who hath enabled me, for that he counted me faithful, putting me into the ministry;
This is a true saying, if a man desire the office of a bishop, he desireth a good work. A bishop then must be blameless, the husband of one wife, vigilant, sober, of good behaviour, given to hospitality, apt to teach; Not given to wine, no striker, not greedy of filthy lucre; but patient, not a brawler, not covetous; One that ruleth well his own house, having his children in subjection with all gravity; (For if a man know not how to rule his own house, how shall he take care of the church of God?)
If thou put the brethren in remembrance of these things, thou shalt be a good minister of Jesus Christ, nourished up in the words of faith and of good doctrine, whereunto thou hast attained. But refuse profane and old wives' fables, and exercise thyself rather unto godliness. For bodily exercise profiteth little: but godliness is profitable unto all things, having promise of the life that now is, and of that which is to come. This is a faithful saying and worthy of all acceptation. For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe. These things command and teach. Let no man despise thy youth; but be thou an example of the believers, in word, in conversation, in charity, in spirit, in faith, in purity. Till I come, give attendance to reading, to exhortation, to doctrine. Neglect not the gift that is in thee, which was given thee by prophecy, with the laying on of the hands of the presbytery. Meditate upon these things; give thyself wholly to them; that thy profiting may appear to all. Take heed unto thyself, and unto the doctrine; continue in them: for in doing this thou shalt both save thyself, and them that hear thee.
Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine.
First Timothy, Catholic chapter one, Protestant verse twelve,
First Timothy, Catholic chapter three, Protestant verses one to five,
First Timothy, Catholic chapter four, Protestant verses six to sixteen,
First Timothy, Catholic chapter five, Protestant verse seventeen,
as authorized, but not authored, by King James