In the old Islamic tradition, an unmarried woman of marriageable age was thought of as being vulnerable to a variety of evils, mainly temptation and unscrupulous men trying to take advantage of a needy female. Therefore, when a man married a woman, he was thought of as having granted her his protection as an adult male who will be responsible for her upkeep and who will jealously guard her honor as his. In this connection, we say that the man extended his protection to her, or سَـتَرَها.

This is what is being hinted at in this passage:
البناء بها وإرخاء السـتر عليها

The first item البناء بها refers to the legal instrument, the marriage contract. The second item, إرخاء السـتر عليها, refers to the social aspect. This implies a favor by the man, but that is another discussion.

There are probably a variety of ways to phrase this in English once you have figured out what is being hinted at. My suggestion is just one possible way.

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Note added at 11 hrs (2020-03-10 07:19:58 GMT)
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So far, two answers seem to suggest that إرخاء السـتر عليها is a euphemism for marital intimacy. Ramadan suggested "consummation," which is pretty direct, and Mai suggested "being alone" with her, which is indirect. If this is more than conjecture, I would surely withdraw my answer above and defer to either of the two answers. Please do your due diligence to verify and then let us know so we can all learn. If it pans out, I would suggest "having marital congress with her." Otherwise, I would stand by my answer. Many thanks for a very interesting question.