Boy terribly shy one in front of papa giving formal address (8)
I believe the answer is:
ladyship
'formal address' is the definition.
(formal address for a noblewoman)
'boy terribly shy one in front of papa' is the wordplay.
'boy' becomes 'lad' (informal term for boy).
'terribly' indicates an anagram.
'one' becomes 'I' (Roman numeral).
'in front of' indicates taking the first letters.
The first letter of 'papa' is 'p'.
'shy' is an anagram of 'ysh'.
'lad'+'ysh'+'i'+'p'='LADYSHIP'
'giving' acts as a link.
(Other definitions for ladyship that I've seen before include "Title used to a woman of rank" , "Female title" , "No way to address a duchess!" , "Respectful address to titled person" , "Her --, respectful term of address" .)