New hairstylist cutting as intensely (9)
I believe the answer is:
thirstily
'intensely' is the definition.
Both the definition and answer are adverbs. Perhaps you can see a link between them that I don't see?
'new hairstylist cutting as' is the wordplay.
'new' indicates an anagram.
'cutting' is a deletion indicator.
'hairstylist' with 'as' taken away is 'hirtylist'.
'hirtylist' anagrammed gives 'THIRSTILY'.
Can you help me to learn more?
(Another definition for thirstily that I've seen is " With eager desire".)