There is out side street residential meter parking at 0.70p per hour Mon – Fri (8.30pm-5.30pm)
Or guest parking permits also available for guests on request;
Visitors’ parking permits can be purchased in books of 10 for £6 and a single visitors’ parking permit will allow 90 minutes of parking in both Permit and Shared Use parking bays

There is also a long stay car park, on Morrison Street, please see the link below

http://en.parkopedia.co.uk/parking/carpark/eicc_the_exchange/eh3/edinburgh/