Clause clear with executor, extremely so (5)
I believe the answer is:
rider
'clause' is the definition.
(I know that rider is a type of clause)
'clear with executor extremely so' is the wordplay.
'clear' becomes 'rid' (synonyms).
'with' is a charade indicator (letters next to each other).
'extremely so' means to remove the middle letters (only the letters at the extremes of the word).
'executor' with its middle taken out is 'er'.
'rid'+'er'='RIDER'
(Other definitions for rider that I've seen before include "One on horse or bike" , "Traveller on horseback" , "Horseman or addendum" , "Comment from jury" , "supported by an Arab, perhaps" .)