It's shut up on many a morning (4)
I believe the answer is:
clam
'morning' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.
'it's shut up on many a' is the wordplay.
'it's shut up' becomes 'cl' (I can't justify this - if you can you should give a lot more credence to this answer).
'on' is a charade indicator (letters next to each other).
'many' becomes 'M' (Roman numeral for a thousand).
'm' put after 'a' is 'am'.
'cl'+'am'='CLAM'
Can you help me to learn more?
(Other definitions for clam that I've seen before include "Burrowing marine mollusc living in sand or mud" , "Aquatic creature" , "Large bivalve mollusc" , "Large shellfish with hinged shell" , "A silent type" .)