I'm in a similar situation (though I'm still an applicant) as my contract ends in two months and my company is already proposing a new one for the next (it's a expat contract as I'm abroad). I can't tell anything to them as I it would definitely put my new contract on the line.
Therefore I can't ask my boss for recommendations and I have asked my former supervisor (same company but different city, and he agreed to not saying anything) and a current colleague that is comprehensive and won't tell anything either.
In conclusion, I have to write the additional essay the reasons why I'm not asking my current supervisor.
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