@Carolyn L.
Selling interests in LLCs and LLPs gets very complicated. This is going to be a long post simply because I want to try to address as many issues as possible. I apologize for the length in advance.
Prior to addressing the issues, I will say that a 1031 exchange will not be possible if you are selling your interest in the partnership. If you were selling your interest in a specific property, it may be possible, but the IRS specifically precludes a 1031 of partnership interest or stocks and bonds.
On to the complications of selling an interest in an LLC or LLP. The major issue here is that your basis in the LLP is in a constant state of flux. If you buy shares of Apple at $100 per share, your basis is $100 per share. When you buy units in an LLP at $100 per unit, your basis is $100 for a short period of time. An LLP is a pass through entity. When the LLP recognizes income, it is allocated to its members which increases a member's basis in the LLP. The member generally is taxable on it even if the member receives no distribution. On the other hand, when losses are allocated, the member suffers a decrease in basis but may be entitled to deduct a loss. Distributions also reduce the members' basis, offsetting the effect of income allocated on the members' basis. Member contributions increase basis (so if you buy more units, your basis will increase). Often overlooked - liabilities incurred by the LLP are allocated among the members, and each member's share of that debt increases basis, even if such member has no liability on the debt. You should have received an annual "Schedule K-1" from the LLP informing the member of these various adjustments.
LLCs and LLPs also adhere to a "blended" tax basis rule. If you purchase an additional share of Apple now at $200 (you now have two shares - one at $100 and one at $200), and you decide to turn right around and sell that additional share, your cost basis is $200 and you would not recognize a gain or loss. However in an LLP, if you buy an additional unit at $200 (you now have a unit at $100 and a unit at $200) your total interest in the LLP is $300. If you turn right around and sell that unit for $200, you are selling 50% of your interest in the LLP which will realize a cost basis of $150 which means you have a $50 capital gain you must pay tax on. This is likely an unrealistic example but it demonstrates how selling your interest in the LLP can affect you tax wise.
When you sell an interest in a LLP, you may have to recognize ordinary income regardless of how long you have held the units. You will recognize ordinary income on the gain to the extent the gain is attributable to "hot assets" (i.e. inventory items and "unrealized receivables") of the LLP. "Unrealized receivables" basically means items that have not been taxed yet. The remainder of the gain will be taxed as a capital gain at favorable rates.
Generally, the maximum long-term capital gain rate on the sale of LLP interests is 20 percent, however, if the LLP holds depreciable real property, then a 25 percent maximum rate may apply to some of the gain as depreciation recapture.
There are a few more issues that may arise but I'm not sure that you will encounter them. You should consult with an attorney and a tax professional that completely understands your situation prior to making your decision.
