How data can be transferred from Sybase SQL Anywhere to SQL Server
Method 1: 

You can create a Linked server at SQL server pointing to SYBASE and then create a SQL server agent job that does the task of refreshing the data from SYBASE to SQL with help of OPENQUERY. This is better explained in the article here.

Method 2:

If you are comfortable at creating SSIS package, then you can create one, in case method 1 cannot be used with security point in concern, to fetch the data from SYBASE to SQL server. You can follow the steps as explained in Extracting data from Sybase SQL Anywhere using SSIS through ODBC.

Method 3:

As you said, you have the access to client server, then you may give a try with option of extracting the data from sybase DB tables with help of writing few line codes using bcp utility into csv or text files on the sybase server or copy that onto SQL server. Once the data has been exported onto SQL server you may import with various option available to import the same text/csv file into SQL server.