Mostly err badly about favourite bird (6,6)
I believe the answer is:
stormy petrel
'bird' is the definition.
(stormy petrel is a kind of bird)
'mostly err badly about favourite' is the wordplay.
'badly' indicates anagramming the letters.
'about' indicates putting letters inside.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'mostly'+'err'='mostlyerr'
'mostlyerr' anagrammed gives 'stormyrel'.
'stormyrel' placed around 'pet' is 'STORMY-PETREL'.
(Other definitions for stormy petrel that I've seen before include "Popular name for sea bird believed to presage bad weather" , "Mother Carey's chicken" , "one likely to cause trouble" , "portent of trouble" , "seabird" .)