Hi Clayton,
At my institution, the clippings would share the same accession number as the album since, while not adhered, they did arrive as part of the album. We do assign sub-numbers, as Vivian suggests, when warranted. For example, we routinely do this for photo albums in the Photography Collection and sketchbooks in the Art Collection.
Best wishes,
Mary Alice Harper
Head of Visual Materials Cataloging
Harry Ransom Center
https://www.hrc.utexas.edu/