Computer place in centre, neat if in need of refreshment (8,4)
I believe the answer is:
internet cafe
'computer place' is the definition.
(place with computers)
'centre neat if in need of refreshment' is the wordplay.
'in need of refreshment' indicates anagramming the letters.
'centre'+'neat'+'if'='centreneatif'
'centreneatif' with letters rearranged gives 'INTERNET CAFE'.
'in' is the link.
(Other definitions for internet cafe that I've seen before include "centre of communications" , "Place for a cuppa and some surfing?" .)