Question: Should a Sefer Torah be covered between aliyot?
Answer: There is not a clear cut halachic view on this matter. The Shuchan Aruch (Orach Chayim 139:5) rules that common custom is to cover a Sefer Torah between aliyot.
The Rema notes that in his area the custom was to roll up the Sefer Torah between aliyot and that is what is important. The Mishnah Berurah (139:21) contends that the Rema implies that covering an open Sefer Torah is not sufficient. It must be rolled up. He cites the Taz that, accordingly, one need not cover a Sefer Torah between aliyot.
However, after Kaddish when the keriah has concluded or when there is a great span of time between aliyot – for example, when calling up a chatan – the custom is to cover a Sefer Torah.
Of interest is the ruling of the Aruch HaShuchan. He notes (Orach Chayim 139:16) that the custom to cover a Sefer Torah implies that the Sefer Torah is left open between aliyot (which is why a cover is necessary). The custom to roll a Sefer Torah, in contrast, implies that no cover is needed altogether.
A third custom is articulated by the Sha’ar Efraim. He notes (4:21) that even though a Sefer Torah is rolled up, it should still be covered because of kavod HaTorah. The Torah should not be uncovered during Mi’shebeirachs.