Oddly, wallaby annoys state capital (6)
I believe the answer is:
albany
'state capital' is the definition.
(Albany is an example)
'oddly wallaby annoys' is the wordplay.
'oddly' means one should take alternating letters.
'wallaby'+'annoys'='wallabyannoys'
The alternating letters of 'wallabyannoys' are 'ALBANY'.
(Other definitions for albany that I've seen before include "Husband of Goneri (Lear)" , "and a third" , "capital in USA" , "American capital" , "Capital of New Yorki state" .)