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' is an anagram indicator.
'into' means one lot of letters goes inside another.
'the arena' becomes 'ring' (I've seen this in other clues).
'as'+'one'='asone'
'asone' is an anagram of 'eason'.
'eason' put inside '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" .)