At first criticise series that is about old archbishop (6)
I believe the answer is:
runcie
'old archbishop' is the definition.
I don't know anything about this answer so I cannot tell whether this works.
'at first criticise series that is' is the wordplay.
'at' says to put letters next to each other.
'first criticise' becomes 'c' (1st letter of 'criticize').
'series' becomes 'run' (a run or sequence of things).
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'c' put after 'run' is 'runc'.
'runc'+'ie'='RUNCIE'
'about' is the link.
Can you help me to learn more?
(Another definition for runcie that I've seen is " Robert -, former Archbishop of Canterbury".)