Inexpensive lodgings (6)
'inexpensive lodgings' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for hostels that I've seen before include "Inexpensive lodgings" , "Places offering cheap accommodation" .)
(Other definitions for hostel that I've seen before include "Temporary home for the hiker" , "Building providing cheap overnight accommodation" , "Cheap accommodation for students, etc" , "Cheap accommodation for traveller or backpacker" , "Cheap lodging-house for young travellers" .)