Manner of saint backing city in Cambridgeshire (5)
I believe the answer is:
style
'manner' is the definition.
(I know that manner can be written as style)
'saint backing city in cambridgeshire' is the wordplay.
'saint' becomes 'st' (abbreviation).
'backing' says the letters should be written in reverse.
'city in cambridgeshire' becomes 'ely' (I've seen this before).
'ely' in reverse letter order is 'yle'.
'st'+'yle'='STYLE'
'of' is the link.
(Other definitions for style that I've seen before include "Designate" , "Vogue or grace" , "Technique" , "Characteristic manner" , "Elan" .)