For Partnership point of View, there are two questions in your query;
1. Whether TDS need to be dedcuted on payment of tour package?
If the bill is coming in the name of Firm and the payment is directly made by firm to travel agent then Yes, TDS will be applicable for firm. It should deduct the TDS otherwise entire amount will be disallowed.
If the bill is in the name of Partner and after making payment from his personal bank, he is claiming the reimbursement, TDS may not be applicable.
2. Whether payment made will be treated as personal expense or business expense. Apparently, the expense appears to be personal in nature and AO can disallow the same but if it can be prooved that journey was for business development or for official purpose, then part of the total expense (on ad-hoc basis) can be disallowed by AO.