Some singular notion that runs through Florence (4)
I believe the answer is:
arno
'that runs through florence' is the definition.
(the River Arno runs through Florence)
'some singular notion' is the wordplay.
'some' says the answer is hidden in the clue (some of the parts of the word are used).
'ARNO' can be found hidden inside 'singular notion'.
(Other definitions for arno that I've seen before include "Italian river" , "River in central Italy" , "River in Tuscany" , "Pisa's river" , "River of 4 down?" .)