What starts with a very enthusiastic greeting (4)
I believe the answer is:
wave
'greeting' is the definition.
(gesture used as a greeting)
'what starts with a very enthusiastic' is the wordplay.
'what starts' suggests taking the first letters (the letter that starts the word).
'very enthusiastic' becomes 've' (this might be a standard abbreviation I've not previously seen).
The initial letter of 'with' is 'w'.
'w'+'a'+'ve'='WAVE'
Can you help me to learn more?
(Other definitions for wave that I've seen before include "Hand gesture - ridge of moving water" , "Drive forward" , "Make hair curl" , "may have a crest at the top?" , "Roller; a gesture" .)