Measure of bridge in Venice announced (4)
I believe the answer is:
size
'measure' is the definition.
(size is a kind of measure)
'bridge in venice announced' is the wordplay.
'bridge in venice' becomes 'Sighs' (the Bridge of Sighs).
'announced' indicates a 'sounds like' (homophone) clue.
'sighs' is a homophone of 'SIZE'.
'of' is the link.
(Other definitions for size that I've seen before include "Dimension" , "Standard measurement" , "stiffener" , "mass" , "Extent; a sealant" .)