Great service provides accommodation for old man quickly (5)
I believe the answer is:
apace
'quickly' is the definition.
(I know that quickly can be written as apace)
'great service provides accommodation for old man' is the wordplay.
'great service' becomes 'ace' (tennis serve).
'provides accommodation for' is an insertion indicator (inserted letters are accommodated).
'old man' becomes 'pa' (both can mean father).
'ace' enclosing 'pa' is 'APACE'.
(Other definitions for apace that I've seen before include "fast" , "(Move on) swiftly" , "Quick" , "flat out" , "Swiftly, quickly" .)