It depends. If you received Form 1065 Schedule K-1 and you were required to pay these expenses under the partnership agreement, you may report your expenses on Schedule E (Partnership Income) as "Unreimbursed Partnership Expenses" (UPE). In this case, TurboTax will ask you about UPE, with follow-up entry at the end of the Schedule K-1 input. There is no IRS limit, although the partnership agreement may specify otherwise.
But if the partnership agreement specifically states that the partnership has a non-reimbursement policy when expenses are incurred outside of the partnership or that it does not specifically require partners to pay for certain expenses, the deduction may be disallowed at the partner level.
Look for the page "Describe the Partnership" during the K-1 interview. Check the box for "I am required to pay supplemental business expenses on behalf of this partnership/LLC for which I am not reimbursed."
See instructions for Form 1040, Schedule E for more info from the IRS.