[en] This study presents the laboratory background measurement of a Clover-type composite γ-detector equipped with a BGO escape-suppression shield. Recently, such a detector had been used in an in-beam γ-spectroscopy measurement of the ¹⁴N(p,γ)¹⁵O reaction deep underground. Here the laboratory γ-ray background of that detector is studied in three different environments: overground, in a shallow underground laboratory and deep underground. In addition, the effect of the escape-suppression shield on the cosmic-ray induced background has been studied in all three cases. The measurements have been performed at LUNA site in the Gran Sasso National Laboratory, Assergi, Italy (deep underground), at the Felsenkeller Laboratory, Dresden, Germany (shallow underground) and ATOMKI, Debrecen, Hungary (Earth's surface).