Irishman hot on the trail (4)
I believe the answer is:
path
'the trail' is the definition.
(thesaurus)
'irishman hot on' is the wordplay.
'irishman' becomes 'pat'.
'hot' becomes 'h'.
'on' means one lot of letters go next to another.
'pat'+'h'='PATH'
(Other definitions for path that I've seen before include "Track; direction" , "Trodden track" , "trail" , "Way for pedestrians" , "Track, way for walkers" .)