Bird appearing regularly in the arena (4)
I believe the answer is:
tern
'bird' is the definition.
(tern is a kind of bird)
'regularly in the arena' is the wordplay.
'regularly in' means one should take alternating letters.
'the'+'arena'='thearena'
The alternate letters of 'thearena' are 'TERN'.
'appearing' acts as a link.
(Other definitions for tern that I've seen before include "Three-masted schooner" , "Seabird related to the gull" , "Gull-like sea bird" , "Sea bird, a small gull" , "Fork-tailed relative of the gull" .)