Has the type already been added to your AOC, approved in the Ops Manual, MCM, etc?
If so the training agreement should make mention that the items specified in the approved COM will be covered.
One of the issues in the past and is still prevalent has been that Canuck Air Ltd has contrated with a third party (Arctic Wolf Air) who also operates the Moose 123A type.
The Canuck Air pilots all head off to the big city located over the horizon for a week or so of expensive hotels, decent food, and beers in the evening, and are trained by Arctic Wolf Air and training records, exam results, etc kept ...... they are Arctic Wolf's forms, SOPs and items from their approved training program, not the approved Canuck Air items, SOPs, records, and forms.
Then after the pilots come home supposedly all trained and race ready to start flying the Moose 123A on line and gaining some cash flow, the pissing match with TC begins and the Canuck Air Ops Mgr is pissed with Transport because they maintain the approved training program wasn't conducted.
Of course, its Transport's fault because everyone knows that the only reason TC staff go to work in the morning is for the joy of finding some new way to screw over everyone in aviation.
The provisions of a typical COM regarding Contract Training is that the forms, syllabus, SOPs, approved ground training, etc of (in our example) Canuck Air will be used. The only thing that changes is it is as if Arctic Wolf Air's training pilot worked for Canuck for a short period.