Young male Yankee offers to trap first of rare beetles (9)
I believe the answer is:
ladybirds
'beetles' is the definition.
(ladybird is a kind of beetle)
'young male yankee offers to trap first of rare' is the wordplay.
'young male' becomes 'lad'.
'yankee' becomes 'y' (phonetic alphabet: alpha, bravo, charlie etc.).
'offers' becomes 'bids' (bid is a kind of offer).
'to trap' indicates putting letters inside.
'first of' says to take the initial letters.
The first letter of 'rare' is 'r'.
'bids' enclosing 'r' is 'birds'.
'lad'+'y'+'birds'='LADYBIRDS'
(Another definition for ladybirds that I've seen is " Spotted beetles that feed on aphids".)