Without hesitation, ask hotel abroad about one (4,1,4)
I believe the answer is:
like a shot
'without hesitation' is the definition.
(I've seen this before)
'ask hotel abroad about one' is the wordplay.
'abroad' is an anagram indicator.
'about' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'ask'+'hotel'='askhotel'
'askhotel' is an anagram of 'lkeashot'.
'lkeashot' enclosing 'i' is 'LIKE A SHOT'.
(Other definitions for like a shot that I've seen before include "enthusiastically?" , "straightaway?" , "looking round, in field event?" , "right now?" , "What tequila drinkers might do" .)