The definition for contemporary is:-
According to dictionary .com, contemporary is a situation of existing , occurring or living at the same time and of the present time.
While according to Oxford Student Dictionary, design is - the way that something is planned, and made or arranged. It also stated that design is also a process and skill of making drawing. ......
So to put it together Contemporary design is a planned process of making drawing that suite the current trend in the present time.
Hand Drawn batik is batik design that is done without the use of block stencil. (Block stensil is copper plate with batik design that is dip in to melted wax and then applied to the surface of a fabric.) This mean any tool that can be use to create batik design is considered hand drawn batik. Examples of such tool are, canting, brush, stick, salt etc.
To clearly defined Contemporary Hand Drawn Batik design is a process of making current batik design using tools beside block stamping. But the most popular tool used is canting and brush.