Hence the classic slogan, "If you find a better whisky, buy it."

hence为连接性副词，表示一种因果关系。即前面一句话的内容为后面一句话的原因，或者说本句是前一句话的结果。本句是个省略句，省略了 there is.

Hence there is the classic slogan, "if you find a better whisky, buy it." 引号内的句子为slogan的同位语。