Person getting irrational after one comes in late? (9)
I believe the answer is:
recipient
'person' is the definition.
(recipient is a kind of person)
'irrational after one comes in late?' is the wordplay.
'irrational' becomes 'pi' (an irrational number).
'after' means one lot of letters go next to another.
'one' becomes 'I' (Roman numeral).
'comes in' is an insertion indicator.
'late?' becomes 'recent' (similar in meaning).
'pi' put after 'i' is 'ipi'.
'ipi' inserted into 'recent' is 'RECIPIENT'.
'getting' is the link.
(Other definitions for recipient that I've seen before include "Receiver" , "Beneficiary" , "Someone getting" , "One taking delivery" , "Person who gets" .)