Irishman, in the main, backed chief points (6)
I believe the answer is:
seamus
'irishman' is the definition.
(common Irish name)
'main backed chief points' is the wordplay.
'main' becomes 'sea' (the main is an old name for the sea).
'backed' says the letters should be written backwards.
'chief points' becomes 'sum' (in sum means just the chief points).
'sum' written backwards gives 'mus'.
'sea'+'mus'='SEAMUS'
'in the' is the link.
(Other definitions for seamus that I've seen before include "- Heaney, Irish poet" , "Irishman?" , "Irish poet, b. 1939" , "Irish form of James" .)