Clean what could be venerated mosaic cross here with due care (7)
I believe the answer is:
rubicon
'cross here with due care' is the definition.
(as in the phrase 'crossing the Rubicon')
'clean what could be venerated mosaic' is the wordplay.
'clean' becomes 'rub' (as in rubbing something to clean it).
'what could be venerated mosaic' becomes 'icon' (a religious icon might be a mosaic).
'rub'+'icon'='RUBICON'
(Other definitions for rubicon that I've seen before include "River, its crossing decisive" , "Point of no return (which Caesar crossed in 49BC)" , "Polish picture depicting ancient" , "Stream in northern Italy" , "Line fatefully gone over" .)