Buffalo Bill's beginning with one child (5)
I believe the answer is:
bison
'buffalo' is the definition.
(I know that buffalo can be written as Bison)
'bill's beginning with one child' is the wordplay.
'beginning' says to take the initial letters.
'with' says to put letters next to each other.
'one' becomes 'i' (Roman numeral).
'child' becomes 'son' (male child).
The initial letter of 'bills' is 'b'.
'b'+'i'+'son'='BISON'
(Other definitions for bison that I've seen before include "Big beast" , "It's a buffalo in America" , "Buffalo (US)" , "Wild ox of the prairies" , "Large humped bovid of N America" .)