A separate service charge will be applied.

Literal

Separately service-fee [object-を] receive-humbly.

申し受けます is a formal/humble way of saying 'we will charge/collect' — 申す (humble speak) + 受ける (receive). サービス料 is 'service charge/fee.' 別に here means 'separately/additionally' rather than the casual 'not particularly.' Business-register Japanese for notices.