Bird's leisure-time pursuit (5)
I believe the answer is:
hobby
'pursuit' is the definition.
(I have seen 'Favourite pursuit ' mean 'hobby' so perhaps 'pursuit' could also mean 'hobby')
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for hobby that I've seen before include "Bird of prey - pastime" , "Favourite pastime" , "pursuit of birdwatcher?" , "Bird - eg bird-watching" , "Favourite pursuit" .)