The first person to turn up in Irish town, someone from the distant past? (7)
I believe the answer is:
caveman
'someone from the distant past?' is the definition.
'the first person to turn up in irish town' is the subsidiary indication.
'the first person' becomes 'me' (first-person pronoun).
'to turn up' says the letters should be written backwards.
'in' is an insertion indicator.
'irish town' becomes 'cavan' (I've seen this before).
'me' reversed gives 'em'.
'em' put within 'cavan' is 'caveman'.
(Other definitions for caveman that I've seen before include "Prehistoric human" , "Van came carrying old cliff dweller" , "he has primitive habits" , "Prehistoric male" , "Prehistoric person" .)