Downfall of bear losing its head (4)
I believe the answer is:
ruin
'downfall' is the definition.
(thesaurus)
'bear losing its head' is the wordplay.
'bear' becomes 'bruin' (bruin is a kind of bear).
'losing its head' means to remove the first letter.
'bruin' with its first letter removed is 'RUIN'.
'of' acts as a link.
(Other definitions for ruin that I've seen before include "fall" , "Spoil, impoverish" , "Irreparably damage" , "Destruction or bankruptcy" , "loss of position" .)