The phrase "to complete the collection" means to obtain or acquire the missing pieces or items needed in order to have a full set or group of something. Full definition
It's the most complete collection of book cover templates out there for indie authors. (bookpromotionhub.com)
This landmark exhibition of 45 works will display what is arguably one of the most complete collections of 19th - century Norwegian and Swiss landscape paintings outside their respective nations. (museumpublicity.com)
This curriculum has been wildly successful and shows the hunger that teachers have for more complete collections of ordered resources. (educationnext.org)