For example, rising in the morning with enthusiasm (7)
I believe the answer is:
eagerly
'with enthusiasm' is the definition.
(I've seen this in another clue)
'for example rising in the morning' is the wordplay.
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'rising' says the letters should be written backwards (going up in a down clue).
'in the' is an insertion indicator.
'morning' becomes 'early' (I am not sure about this - if you are sure you should believe this answer much more).
'eg' reversed gives 'ge'.
'ge' placed into 'early' is 'EAGERLY'.
Can you help me to learn more?
(Other definitions for eagerly that I've seen before include "Keenly" , "With keen anticipation" , "Fervently" , "In a keen manner" , "Enthusiastically" .)