Burns character - panicked horseman that gets horse docked (3,8)
I believe the answer is:
tam oshanter
'horseman that gets horse docked' is the definition.
The definition suggests a singular noun which matches the answer.
'burns character panicked' is the wordplay.
I cannot really understand how this works, but
'character' could be 'amos' (I have seen 'Biblical character' mean 'amos' so perhaps 'character' could also mean 'amos') and 'amos' is found within the answer.
This explanation may well be incorrect...
(Other definitions for tam oshanter that I've seen before include "Round Scottish cap" , "Poem by Burns; bobble cap" , "Headgear" , "Poetic hero" , "went to his head?" .)