One over-publicising quote for web-based facility (9)
I believe the answer is:
hypertext
'web-based facility' is the definition.
(internet term)
'one over-publicising quote' is the wordplay.
'one over-publicising' becomes 'hyper' (someone hyping something up).
'quote' becomes 'text' (piece of text).
'hyper'+'text'='HYPERTEXT'
'for' acts as a link.
(Other definitions for hypertext that I've seen before include "A website technology" , "Software system" .)