One brief scare after female called for perfume (10)

'perfume' is the definition.
(perfume made from the frangipani tree)

'one brief scare after female called' is the wordplay.
'one' becomes 'i' (roman numeral).
'brief scare' becomes 'pani' (I am not sure about this - if you are sure you should believe this answer much more).
'after' means one lot of letters go next to another.
'female' becomes 'f' (common abbreviation).
'called' becomes 'rang' ('ring' can be a synonym of 'call').
'i'+'pani'='ipani'
'f'+'rang'='frang'
'ipani' put after 'frang' is 'FRANGIPANI'.

'for' acts as a link.