你的问题可能有两种情况.
1.如果申请已经递交给海关了,可以说：Our application to the Customs is in the process of examination. We shall inform you of the result as soon as possible.
2.如果申请还在书写中,尚未交给海关.也是“正在向海关申请当中”.
这时,可以说：We are making application to Customs for the issue and we shall inform you of the result as soon as possible.