Venetian prince has daughter to avoid (5)
I believe the answer is:
dodge
'avoid' is the definition.
(dodge can mean to avoid or evade)
'venetian prince has daughter' is the wordplay.
'venetian prince' becomes 'doge' (I can't explain this - if you can you should believe this answer much more).
'has' indicates putting letters inside.
'daughter' becomes 'd' (genealogical abbreviation).
'doge' enclosing 'd' is 'DODGE'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for dodge that I've seen before include "Avoid or attempt to" , "Avoid - ruse" , "A quick evasive movement" , "Sidestep with trick?" , "Evade cunningly" .)