Chap from Irish county eager at first to tour North Carolina (8)
I believe the answer is:
clarence
'chap' is the definition.
'irish county eager at first to tour north carolina' is the wordplay.
'irish county' becomes 'clare' (County Clare in Ireland).
'at first' says to take the initial letters.
'to tour' is an insertion indicator (to tour can mean to go around).
'north carolina' becomes 'NC' (abbreviation).
The first letter of 'eager' is 'e'.
'clare'+'e'='claree'
'claree' going around 'nc' is 'CLARENCE'.
'from' is the link.
(Other definitions for clarence that I've seen before include "He was supposedly drowned in malmsey" , "boy" , "Duke drowned in a butt of Malmsey" , "Horse-drawn carriage; man's name" .)