Old flame - the snake - has given sweetheart review that will infuriate her (10)
I believe the answer is:
exasperate
'will infuriate her' is the definition.
I can't judge whether this definition defines the answer.
'old flame the snake has given sweetheart review' is the wordplay.
'old flame' becomes 'ex' (a former partner).
'the snake has given' becomes 'asp' (I can't justify this - if you can you should believe this answer much more).
'sweetheart' becomes 'e' (the middle letter or heart of 'sweet').
'review' becomes 'rate' (I've seen this in another clue).
'ex'+'asp'+'e'+'rate'='EXASPERATE'
'that' is the link.
Can you help me to learn more?
(Other definitions for exasperate that I've seen before include "Drive to distraction" , "bug" , "Intensely irritate" , "Annoy" , "Infuriate" .)