Comments on your issue:

• While you did not technically sell or liquidate the "old" partnership interest you will need to handle it in TT as if you did sell it.  This is the only way to eliminate it from your return going forward.
• As a partner in a partnership you should be maintaining your basis in this investment.  Hopefully you have this.
• My recommendation is to indicate in TT that you disposed of and sold your interest.  In order to not generate any gain or loss, just use your tax basis as the selling price.  Since your basis and selling price will be the same, no gain or loss will be recognized.
• Now for the technical issues.  When you contributed property to a partnership and the FMV is not equal to your basis, then there are special rules that need to be addressed.  These rules fall under Section 704(c) and also the built-in gain or loss rules.  These can be complicated and not really something that can be discussed in a forum such as this.  I recommend you follow-up on these issues and possibly consult with a tax professional to make sure it is handled correctly.
• Finally, your beginning tax basis in the new partnership is your tax basis in the partnership interest you contributed.