Is it possible to add another Contact Field to CiraSync sync tasks? If yes, how can I do this?

Yes, you can sync contact fields besides the defaults by doing the following:

1. Click the account username at the top-right corner of the CiraSync dashboard.
2. Click SETTINGS. 
3. Click Contact Fields.
4. Find the contact field you would like to sync.
5. Click the checkboxes under Write and Overwrite. 
6. Click SAVE in the top-right corner of the dashboard.