Rare blemish creates exasperation initially (6)
I believe the answer is:
scarce
'rare' is the definition.
('scarce' can be similar in meaning to 'rare')
'blemish creates exasperation initially' is the wordplay.
'blemish' becomes 'scar' (scarring is a kind of blemishing**).
'initially' suggests taking the first letters.
The initial letters of 'creates exasperation' is 'ce'.
'scar'+'ce'='SCARCE'
(Other definitions for scarce that I've seen before include "Not plentiful, hard to find" , "Deficient in quantity" , "Not often found" , "Not enough to satisfy demand" , "Common? Definitely not" .)