An important aspect of this passage it that it has a structure frequently found in the Bible known as a 'chiastic structure'. It works in layers towards a centre, and then back out again. Another important point is the word 'likewise' in verse 8 & 11 is the same Greek word we encountered last week, that acts like a short circuit between the sections. So whatever Paul says about elders he also says about deacons and about female leaders - the principles apply across the board.
Those principles are character, character and character. How a person conducts themselves, how they behave, is of primary importance. There is no blueprint for positions or roles in the church (like fabric deacon or treasurer!), but a requirement to be respectable, faithful in their marriage, hospitable and so on.
We know this makes sense: in our society a leader simply cannot remain in their position if they behaviour doesn't add up. Ultimately leaders lead by example and not clever words - the things a leader wants to impart are caught, not taught, so their conduct is of paramount importance.
An interesting way to look at the character traits Paul lists is how they relate to honouring other people. For example being faithful to your spouse and having respect of your children are about how you are with your nearest. Being temperate and self-controlled are about how you conduct yourself under pressure - are you still able to honour those around you in those circumstances. Being hospitable is about an openness to others, being able to honour the stranger. Sincerity, not malicious in your talk, and being worthy of respect also reflect honour for others, which earns you respect (and thus honour) from others.
The initial verses are complemented by the latter verses, working towards the centre which is verse 9 & 10: 'keep hold of the deep truths of the faith'. Remember these letters are about combating people who have got the wrong idea and are departing from the truth, so Timothy is to look for leaders who are well connected to their foundations in Jesus - their character will flow from this.
A CEO of a major secular company once said 'Hire for attitude, train for skills'. If their foundation is right, you can train them up in the things they will need to do. This is true for Christian leaders - if their foundation in Jesus is right they can then learn the skills they will need. Note v2 'able to teach' can also be 'potential to teach', an ability to learn ... but that requires the person is teachable. The worst thing is people who are simply not teachable - there is little you can do with them. This resonates with the principle we had earlier in the year that discipleship involves correcting and restoring, which needs an open leader and teachable learner to travel together on the journey of discipleship.
The final verse v13 balances the first verse v1. Although v1 sounded secular its counterpart v13 is thoroughly spiritual, about serving (not lording), sure faith in Jesus, and standing tall in that faith. Put the two together and we get something like:
Here is a trustworthy saying: whoever aspires to be a leader desires a noble task - that if you serve in well will be one that stands out, being confident and sure in faith in Christ Jesus
That is something great for other Christians to be influenced by and copy into their own lives. And as v15 says, if the whole body of Christians live like this it is a wonderful sight, giving a prominent temple-like pillar and firm foundation for everyone else to see.