Like that business opening tomorrow in course? (5)
I believe the answer is:
ascot
'course?' is the definition.
(Ascot is a racecourse)
'like that business opening tomorrow' is the wordplay.
'like' becomes 'as'.
'that business' becomes 'co' (short for company).
'opening' indicates taking the first letters.
The first letter of 'tomorrow' is 't'.
'as'+'co'+'t'='ASCOT'
'in' acts as a link.
(Other definitions for ascot that I've seen before include "Horse-racing venue" , "Tie round the neck" , "track" , "course without any fences!" , "Berkshire race course" .)