As IrwinMFletcher rightly says - it sounds like you want Music on Hold - MoH - (once the Mitel phone person has put them on hold)
Either an external MoH source (eg CD Player plugged into the Cinch (?) socket at the back of the Mitel plus a bit of programming to state that the music on hold source is External and the port that it is on is some sort of analogue trunk*
or
upload a WAV file (look for system audio settings or something similar)
Wav files have to be in a very specific format and then, in order to upload them, you normally have to lower all internet settings (tools, options, trusted sites, add the Mitel ip address, lower the settings to lowest)
*All exact info is in the help / admin once you are connected to the Mitel.
You can download a converter form the internet - such as "ease audio converter" which will convert a standard music file to a Mitel-compatible one - the size of it normally has to be quite small.
Als,. similar to the the CD player option, set the music on hold source to embedded.