Arrived, having done away with singular cryptic handles (4-5)
I believe the answer is:
code-names
'cryptic handles' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.
'arrived having done away with singular' is the wordplay.
'arrived' becomes 'came' (come can mean to appear or arrive).
'having' is an insertion indicator.
'away' indicates an anagram (letters move away from their original places).
'with' is a charade indicator (letters next to each other).
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
'done' is an anagram of 'oden'.
'came' enclosing 'oden' is 'codename'.
'codename'+'s'='CODE-NAMES'
Can you help me to learn more?