Air-conditioning in car starts to tickle your cheek (8)
I believe the answer is:
audacity
'cheek' is the definition.
(audacity is a kind of cheek)
'air-conditioning in car starts to tickle your' is the wordplay.
'air conditioning' becomes 'AC'.
'in' indicates putting letters inside.
'car' becomes 'audi' (Audi is a German car brand).
'starts to' says to take the initial letters.
The initial letters of 'tickle your' is 'ty'.
'ac' placed into 'audi' is 'audaci'.
'audaci'+'ty'='AUDACITY'
(Other definitions for audacity that I've seen before include "Cheek, nerve" , "Effrontery" , "Courage" , "Boldness - such nerve!" , "Temerity" .)