Lobby leaders on universally marketing Irish cheese (8)
I believe the answer is:
halloumi
'cheese' is the definition.
(I've seen this before)
'lobby leaders on universally marketing irish' is the wordplay.
'lobby' becomes 'hall' (synonyms).
'leaders' suggests taking the first letters.
The first letters of 'on universally marketing irish' is 'oumi'.
'hall'+'oumi'='HALLOUMI'
(Other definitions for halloumi that I've seen before include "Greek dish of fried goat's cheese" , "Cheese from Cyprus" , "Traditional Cypriot cheese" , "Cypriot goat's or sheep's milk cheese" .)