I was first to be going around shop (4)
I believe the answer is:
deli
'shop' is the definition.
(I've seen this before)
'i was first to be going around' is the wordplay.
'was first' becomes 'led'.
'to be going around' says the letters should be written in reverse.
'i'+'led'='iled'
'iled' reversed gives 'DELI'.
(Other definitions for deli that I've seen before include "food-store?" , "Special shop" , "shop briefly" , "Fine foods shop" , "place to buy food" .)