Adam Clarke on Hebrews 13:18

Pray for us - Even the success of apostles depended, in a certain way, on the prayers of the Church. Few Christian congregations feel, as they ought, that it is their bounden duty to pray for the success of the Gospel, both among themselves and in the world. The Church is weak, dark, poor, and imperfect, because it prays little.

We trust we have a good conscience - We are persuaded that we have a conscience that not only acquits us of all fraud and sinister design, but assures us that in simplicity and godly sincerity we have labored to promote the welfare of you and of all mankind.

To live honestly - Εν πασι καλως θελοντες αναστρεφεσθαι· Willing in all things to conduct ourselves well - to behave with decency and propriety.