Falcon’s pursuit (5)
I believe the answer is:
hobby
This clue is a double definition.
'falcon's' is the first definition.
(hobby is a kind of falcon)
'pursuit' is the second definition.
(I know that pursuit can be written as hobby)
(Other definitions for hobby that I've seen before include "Bird of prey - pastime" , "interest" , "Raptor - pastime" , "Small falcon" , "Favourite pursuit" .)