This Ticket of Leave Register for the York District is for 1872 - 1887. It can be viewed on microfilm at the State Library of Western Australia. Look for Series 1660 Cons 5225/1.
You can check which page your convict is on by downloading the index which we have created from this link FamilyHistoryWA Convict Related Stories. Look at the bottom of the page to download the spreadsheet.