The old() helper only returns the value selected before a validation error occurred.
If you have a default value then you add it as the second parameter for old
You also need to name your input field. I would stick to the same naming convention as the db column that the result goes into.
Finally, you can use @selected blade helper so that you end up with something like;
<select id="Priority_id" style="width:180px;" class="myform-select" name="Priority_id">
<option>Select priority</option>
@foreach ($priorities as $priority)
<option value="{{ $priority->id }}" @selected( old('Priority_id', $model->priority)==$priority->id) >
{{ $priority->Desc }}
</option>
@endforeach
</select>