Designated driver's offer (4)

I believe the answer is:

ride

(Other definitions for ride that I've seen before include "Fairground attraction; go on horseback" , "Eg, roundabout or roller-coaster, path for horses" , "Travel in or be carried on" , "Journey on horseback" , "Travel on the back of animal" .)

I've seen this clue in the USA Today.

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