Measure frill worn by Lucinda periodically (5,5)
I believe the answer is:
fluid ounce
'measure' is the definition.
(fluid ounce is a kind of measure)
'frill worn by lucinda periodically' is the wordplay.
'frill' becomes 'flounce' (synonyms).
'worn by' is an insertion indicator (outside letters are worn by those on the inside).
'periodically' means one should take alternating letters (letters must be selected 'every so often').
The alternate letters of 'lucinda' are 'uid'.
'flounce' enclosing 'uid' is 'FLUID OUNCE'.
(Other definitions for fluid ounce that I've seen before include "volume of water?" , "a little liquid" .)