Outgoing leader old and new on throne better (6,4,5)

'throne better' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'outgoing leader old and new on' is the wordplay.
I cannot quite understand how this works, but
'leader' could be 'trump' (Donald Trump) and 'trump' is present in the answer.
'old' could be 'o' (common abbreviation eg in OE for Old English) and 'o' is located in the answer.
an anagram of 'and' is 'dna' which is within the left over letters.
'new' could be 'n' (common abbreviation eg NT for New Testament) and 'n' is found within the answer.
'on' could be 'o' (I've seen this in other clues) and 'o' is found in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?