For this type of activity, you need to have proper legal agreement. You need to make a list of the services that service provider needs to provide, where he will provide, how he will provide, when he will provide, how hus quality of work will be measured, how his invoice will be processed and what will be the payment terms. In addition to this, you need to anticipate the communication requirements between both of you and you need to place as appendix the format of the various reports and returns.
Your attempt should be to make the agreement as foolproof as possible. This will help you in avoiding the disputes in future.
Let me understand whether you want to do the task for your company where you are working or to act on behalf of a company as consultant. The requirement for both are different as having legal implications.
If you are doing it for your company as a staff needs a 'Letter of Authorisation' from the employer if it is apart from your regular task.
On second case, ask the agency to issue LOI or Work Order which will have all the terms of condition[Job description, Do's, Dont's, Duration, Terms of payment & many more things and termination clause]for the task you are going to perform on their behalf. You need to consult a Lawer before accepting the task, in general LOI or Wo is issued after having a joint discussion or meeting on subjected matter. While doing such meeting always accompany with one who is thorough on subjected matter or do the beforehand preparation to avert future problem, whensomething is new to you.
Instead of calling it a letter of authorization in common parlance it is referred as Work order/agreement.
Some hiring consultants do have a format of enrollment with them, try with them also.
Or else you can creat on your own with all terms.
It simply should be a agreement format with all terms and conditions mentioned with validity period and duly executable, as advised by our seniors here.
The contents can differ basing on your type of industry (manufacturing,software,BPO etc)