You can deduct unreimbursed ordinary and necessary partnership expenses you paid on behalf of the partnership if you were required to pay these expenses under the partnership agreement (except amounts deductible only as itemized deductions, which you must enter on Schedule A).
Enter your Partnership K-1 first, then create a second partnership record to enter the unreimbursed partnership expenses. Enter UPE (unreimbursed partnership expenses) as the Name of Partnership. Enter the amount of the unreimbursed job expenses as a loss on the Ordinary Business Income (Loss) line with a negative sign in front of the expense number so it is treated as a loss. This will make the unreimbursed partnership expenses show up on a separate line than your regular partnership K-1 income on Schedule E page 2 of your tax return which is how the IRS wants it shown.