Do better than Spurs, say, almost unexpectedly (7)
I believe the answer is:
surpass
'do better than' is the definition.
(I've seen this before)
'spurs say almost unexpectedly' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'unexpectedly' indicates an anagram.
'spurs'+'say'='spurssay'
'spurssay' with its last letter removed is 'spurssa'.
'spurssa' anagrammed gives 'SURPASS'.
(Other definitions for surpass that I've seen before include "Transcend" , "Go one better" , "Outdo" , "Be better than (another)" , "eclipse visible" .)