Use the rat-run possibly, making journey with a purpose (8,4)
I believe the answer is:
treasure hunt
'journey with a purpose' is the definition.
(journey to find treasure)
'use the rat-run possibly' is the wordplay.
'possibly' indicates an anagram.
'use'+'the'+'rat'+'run'='usetheratrun'
'usetheratrun' with letters rearranged gives 'TREASURE HUNT'.
'making' acts as a link.
(Other definitions for treasure hunt that I've seen before include "Game where players try to find things by following a series of clues" , "Game searching for hidden objects" , "Children's party game where things are sought" , "Game in which players search for hidden objects by following a trail of clues" , "Search conducted at children's birthday parties" .)