I perceive from your question that you are referring to a particular situation that you are familiar with.  I will assume that you know someone who is a preacher but is separated from his wife…and that he is spending time with another woman.  I hope I have understood your question correctly so I can offer a scriptural answer. 

Let’s begin by reading the portion you referenced.  1 Timothy 3:1-7 says, “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?) Not a novice, lest being lifted up with pride he fall into the condemnation of the devil. Moreover he must have a good report of them which are without; lest he fall into reproach and the snare of the devil.” 

In the Bible, we see that church leadership is entrusted to the bishops, or elders in the local church.  Reading Titus 1:5 and 7, we see the word ‘bishop’ and ‘elder’ is interchanged, showing they refer to the same work.  The Greek word for elder is ‘presbýteros’ which refers to the rather advanced age of the person.  The Greek word for bishop is ‘epískopos’ which refers to the work of an overseer.  In fact, the word ‘epískopos’ is translated as overseer in Acts 20:28. 

I understand your concern about spiritual leaders in the church.  Given the qualifications given in 1 Timothy 3:1-7 and in Titus 1:6-9, we see the seriousness of one who would take on the role of being a spiritual leader to a local group of believers.  We read more about this needed work in 1 Peter 5:1-3, “The elders which are among you I exhort, who am also an elder, and a witness of the sufferings of Christ, and also a partaker of the glory that shall be revealed: Feed the flock of God which is among you, taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind; Neither as being lords over God’s heritage, but being ensamples to the flock.”

It is a sad thing when our leaders fall or succumb to life’s temptations.  For a leader (or any Christian) to be separated from his wife could be an indication of a home life that is not honoring to the Lord.  The Bible refers to a married couple as being “one flesh”. (Ephesians 5:31).  It is possible that the leader you are referring to is completely innocent and his wife left against his will, but still, it is a sad state when two believers cannot, or will not, abide by the vows they took when they were married.  Perhaps there needs to be time taken off so these two can receive needed counsel to mend their marriage and begin to live together to honor the Lord once more.

We are exhorted in 1 Thessalonians 5:22 to, “Abstain from all appearance of evil.”  For this leader to be spending so much time with another woman while separated from his wife could give the appearance of inappropriate behavior.  That should be avoided at all costs.  Years ago, my wife and I worked with two other women who were close friends.  Often, we would all eat lunch together at a local restaurant while at work.  If there were days my wife could not join us, I would not eat lunch with the two ladies, just to avoid the appearance of evil.  When our testimony is damaged by bad behavior, it is very difficult to gain a proper testimony back.

Have you, or anyone else, approached this preacher about his situation and his behavior?  There are proper scriptural procedures to be carried out in a situation like this.  I encourage you to read Matthew 18:15-20 for Biblical instruction.  Of course, I encourage you to be praying for this man and his wife that the Lord might come in and save this marriage.  (CC)  (734.2)