My dad, drunk around one, or noon! (6)
I believe the answer is:
midday
'noon' is the definition.
('midday' can be a synonym of 'noon')
'my dad drunk around one' is the wordplay.
'drunk' indicates an anagram.
'around' indicates putting letters inside.
'one' becomes 'i' (Roman numeral).
'my'+'dad'='mydad'
'mydad' with letters rearranged gives 'mdday'.
'mdday' going around 'i' is 'MIDDAY'.
'or' is the link.
(Other definitions for midday that I've seen before include "Twelve noon" , "1200 hours" , "12 o'clock in the day" , "12 noon" , "time when hands are joined" .)