Face granny, extremely close (5)
I believe the answer is:
muggy
'close' is the definition.
(thesaurus)
'face granny extremely' is the wordplay.
'face' becomes 'mug' (mug is a kind of face).
'extremely' says to hollow out the word (remove centre letters).
'granny' with its centre taken out is 'gy'.
'mug'+'gy'='MUGGY'
(Other definitions for muggy that I've seen before include "close" , "Warm and humid" , "Damp and stifling" , "Unpleasantly humid" , "Warm and wet" .)