Group touring Asian city sent the wrong way — that's painfully irritating (4,3)
I believe the answer is:
tear gas
'that's painfully irritating' is the definition.
(tear gas causes painful irritation)
'group touring asian city sent the wrong way' is the wordplay.
'group' becomes 'set' (both can mean a collection).
'touring' means one lot of letters goes inside another (touring can mean going round).
'asian city' becomes 'Agra' (Indian city).
'sent the wrong way' says the letters should be written backwards.
'set' going around 'agra' is 'sagraet'.
'sagraet' in reverse letter order is 'TEAR-GAS'.
(Other definitions for tear gas that I've seen before include "It causes temporary blindness" , "Used by police against rioters, irritates eyes" , "Riot control weapon" , "Riot control means" , "It's eye-watering stuff" .)