Working out as one wanders into the arena (9)
I believe the answer is:
reasoning
'working out' is the definition.
'as one wanders into the arena' is the wordplay.
'wanders' indicates anagramming the letters.
'into' means one lot of letters goes inside another.
'the arena' becomes 'ring' (eg a boxing ring).
'as'+'one'='asone'
'asone' with letters rearranged gives 'eason'.
'eason' going within 'ring' is 'REASONING'.
(Other definitions for reasoning that I've seen before include "Thinking that is coherent and logical" , "Thinking coherently and logically" , "sense?" , "Train of thought" , "Debating" .)