No special trekking permits are required to trek in Bhutan. With your general Bhutan visa you can do trekking in Bhutan.
However you must book your Bhutan trekking tour with a Licensed Bhutanese tour operators (like See Bhutan Travels) and must processed your Bhutan visa prior to your arrival in Bhutan.
Your respective tour operators will process your Bhutan visa upon sending a scanned copy of your passport photo page, Bhutan visa fee of $40 per person and your entire tour payment in advance.
Bhutan does not have a system of issuing visa on arrival.