Father carrying flightless bird’s bone (5)
I believe the answer is:
femur
'bone' is the definition.
(I know that femur is a bone)
'father carrying flightless bird's' is the wordplay.
'father' becomes 'fr' (abbreviation as in a priest's title).
'carrying' means one lot of letters goes inside another.
'flightless bird' becomes 'emu' (emu is a kind of flightless bird).
'fr' enclosing 'emu' is 'FEMUR'.
(Other definitions for femur that I've seen before include "Thighbone" , "Part of leg" , "bit of leg" , "Large bone" , "Bone in leg" .)