Old boy almost furious about forgetfulness (8)
I believe the answer is:
oblivion
'forgetfulness' is the definition.
(oblivion is a kind of forgetfulness)
'old boy almost furious about' is the wordplay.
'old boy' becomes 'ob' (abbreviation).
'almost' means to remove the last letter (most of the word but not all of it).
'furious' becomes 'livid' (both can mean very angry).
'about' becomes 'on' (as in a book 'on' a certain topic).
'livid' with its last letter taken off is 'livi'.
'ob'+'livi'+'on'='OBLIVION'
(Other definitions for oblivion that I've seen before include "State of being forgotten or unconscious" , "Insensibility" , "State of total unconciousness" , "Obscurity" , "State of being totally forgotten" .)