Set off, eager to arrange cheap accommodation (8)
I believe the answer is:
steerage
'cheap accommodation' is the definition.
(I've seen this before)
'set off eager to arrange' is the wordplay.
'off' indicates an anagram.
'to arrange' is an anagram indicator.
'set' with letters rearranged gives 'ste'.
'eager' with letters rearranged gives 'erage'.
'ste'+'erage'='STEERAGE'
(Other definitions for steerage that I've seen before include "Cheapest accommodation in old passenger ships" , "Course" , "Cheapest part of liner" , "Densely-packed travellers here" , "Formerly cheapest space on board" .)