A rum old collection assembled bit by bit (7)
I believe the answer is:
modular
'assembled bit by bit' is the definition.
'a rum old collection' is the wordplay.
'collection' is an anagram indicator (the same collection of letters).
'a'+'rum'+'old'='arumold'
'arumold' with letters rearranged gives 'MODULAR'.
(Other definitions for modular that I've seen before include "in several parts" , "Built from separate units" , "Made of units" , "Made from detachable pieces" .)