There are several options for accessing the Art Newspaper:
Art & Architecture Source December 2006 onwards. Easier to search than the free archive, though a few articles, especially short pieces, may be missing. Available to SIA staff and students. Includes details, though not text, of many articles from previous years, though coverage is inconsistent in coverage. If you discover an article you are interested in this way, cross-check with the free archive or SIA's collection on paper.
On paper in the SIA library Issue 1 (1990) onwards. A few issues are missing, so please check the link.
Free website with many of the AN's current stories. From here you can sign up for the free newsletter, which is supplementary to the Newspaper itself.
Email newsletter free newsletter, supplementary to the Newspaper itself
A personal subscription may be a worthwhile investment for you, and gives you both a paper copy and a PDF.