Offer made by barman in dramshop eagerly? (4,1,4)
I believe the answer is:
like a shot
'eagerly?' is the definition.
(I've seen this before)
I don't understand how the remainder of the clue works.
(Other definitions for like a shot that I've seen before include "What spirit drinkers do" , "straightaway?" , "show partiality for spirits" , "sluggish?" , "enthusiastically?" .)