Beast turning up —- turning up in the morning (4)
I believe the answer is:
puma
'beast' is the definition.
(puma is an animal)
'turning up turning up in the morning' is the wordplay.
'turning' is a reversal indicator.
'turning up in' says the letters should be written backwards.
'the morning' becomes 'am'.
'up' in reverse letter order is 'pu'.
'am' reversed gives 'ma'.
'pu'+'ma'='PUMA'
(Other definitions for puma that I've seen before include "Cougar" , "Mountain lion" , "Large American feline resembling a lion" , "Large Am. wild cat" , "South American carnivore" .)