Reluctant to quote over cutting housing cost (8)
I believe the answer is:
reticent
'reluctant' is the definition.
(reticent means reluctant to talk)
'quote over cutting housing cost' is the wordplay.
'quote' becomes 'cite' (synonyms).
'over' shows that the letters should be reversed in order.
'cutting' is an insertion indicator (some letters cut their way into a word).
'housing cost' becomes 'rent' (cost of renting a house).
'cite' backwards is 'etic'.
'etic' put into 'rent' is 'RETICENT'.
'to' acts as a link.
(Other definitions for reticent that I've seen before include "Reserved, shy" , "Reserved, loath to talk" , "Not wanting to talk" , "Uncommunicative" , "Reserved, not revealing thoughts readily" .)