You Can take Ola or Uber from Chandigarh Airport . Below are the Taxi fares from Chandigarh Airport to Manali.
SUV - Xylo / Ertiga / Similar - Rs 7019 aprox.
Hatchback - Ritz / Indica / Similar - Rs 5300 aprox.
Sedan - Swift Dzire / Toyota Etios / Similar- Rs 5390 aprox.