Fossil, a little one with day inscribed (8)
I believe the answer is:
ammonite
'fossil' is the definition.
(ammonite is a kind of fossil)
'a little one with day inscribed' is the wordplay.
'a little' means to remove the last letter (the word is not quite complete).
'one' becomes 'an' (an apple is one apple).
'with' means one lot of letters goes inside another.
'day' becomes 'mon' (short for Monday).
'inscribed' becomes 'mite' (I can't justify this - if you can you should give a lot more credence to this answer).
'an' with its last letter taken away is 'a'.
'mon' inserted inside 'mite' is 'mmonite'.
'a'+'mmonite'='AMMONITE'
Can you help me to learn more?
(Other definitions for ammonite that I've seen before include "Coiled fossil shell of extinct mollusc" , "Type of explosive" , "Type of fossil" , "Common fossil" , "old nomadic tribesman" .)