Fine appointment about lice problem (8)
I believe the answer is:
delicate
'fine' is the definition.
(similar in meaning)
'appointment about lice problem' is the wordplay.
'appointment' becomes 'date' (synonyms).
'about' means one lot of letters goes inside another.
'problem' indicates an anagram.
'lice' anagrammed gives 'elic'.
'date' going around 'elic' is 'DELICATE'.
(Other definitions for delicate that I've seen before include "Fine and dainty" , "Flimsy" , "Fragile - tactful" , "Discriminating" , "Soft" .)