Quiet female leading old chaps on -- remarkable thing (10)
I believe the answer is:
phenomenon
'remarkable thing' is the definition.
(I've seen this before)
'quiet female leading old chaps on' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano').
'female' becomes 'hen' (hen is a kind of female**).
'leading' indicates taking the first letters.
'chaps' becomes 'men' (I've seen this before).
The first letter of 'old' is 'o'.
'p'+'hen'+'o'+'men'+'on'='PHENOMENON'
(Other definitions for phenomenon that I've seen before include "Wonder" , "Remarkable occurrence" , "(Remarkable) happening" , "Observable event" , "rarity" .)