Private eye covering alphabet initially hopes to get a flyer (8)
I believe the answer is:
dabchick
'private eye' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.
'covering alphabet initially hopes to get a flyer' is the wordplay.
'covering' is an insertion indicator.
'alphabet' becomes 'abc' (I've seen this before).
'initially' suggests taking the first letters.
'to get a flyer' becomes 'dick' (I can't justify this - if you can you should believe this answer much more).
The first letter of 'hopes' is 'h'.
'abc'+'h'='abch'
'abch' going into 'dick' is 'DABCHICK'.
Can you help me to learn more?
(Other definitions for dabchick that I've seen before include "good swimmer and diver" , "diving-bird" , "Waterbird" , "Small grebe" , "Water bird - little grebe" .)