St Paul also suggests that periods of abstinence can be beneficial. Additionally, while it isn’t talked about much now, it used to be encouraged that couples practice abstinence at times; during Lent, Fridays, pre-Mass fasts. These were all times when no sex was the norm. And couples used to be told it was avery good thing to choose to live as “brother and sister” once childbearing was done. Not that it was required, but it could be a good choice for some. (The Orthodox are always abstinent when they fast, which is half the year. You might look to see if any Orthodox writings have good practical advice on this issue.)
I think you need to consider what the problems with no sex are, and what the advantages, and how you can minimize the former and take advantage of the latter.
Obviously, it can be hard tot to have an outlet to sexual desires, and that can lead a person into temptation. Most of the strategies for that are the same ones employed by any celibate person. A time of temptation is not necessarily a negative thing though - remember that it was very important in the life of Christ, and many other Saints. It can give great spiritual benefits. (I love the story of St Dunstan.)
As well, that can make one partner feel resentful toward the other, even if he or she knows it is silly. Sex can sometimes bring the couple together or smooth things over in times of difficulty. It is a way to bring intimacy, and can be especially important to very tactile people.
So - you will need to develop ways to do these things without that kind of physical intimacy. You can treat that as a disaster, or as an opportunity. Pray together, take time to do things that have meaning for you that you enjoy, talk, whatever. You will need to put time and effort into it, or you will indeed drift apart.
Try not to cut out all physical affection, though especially at first, it can be hard when you really want sex. But people also need non-sexual touch and affection to thrive.