The story of my possibly fearless father! (4)
I believe the answer is:
myth
'the story' is the definition.
(myth is a kind of story)
'my possibly fearless father' is the wordplay.
'possibly fearless father' becomes 'th' (I can't justify this - if you can you should believe this answer much more).
'my'+'th'='MYTH'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for myth that I've seen before include "Unfounded belief" , "Fancy" , "lie!" , "Legend, folk tale" , "Common false belief" .)