Airline - the ultimate in losing luggage! (3)
I believe the answer is:
bag
'luggage' is the definition.
(bag is a kind of luggage)
'airline the ultimate in losing' is the wordplay.
'airline' becomes 'BA' (British Airways).
'the ultimate in' suggests the final letters (take the ultimate ie last letter).
The final letter of 'losing' is 'g'.
'ba'+'g'='BAG'
(Other definitions for bag that I've seen before include "Pouch" , "Carrier" , "Flexible container for shopping" , "Container for holding or carrying" , "Gladstone, for example" .)