Can I take a part payment from my customer now and collect the rest closer to the travel date?

Yes, in most cases you can take a part payment now and collect the balance later, but what your supplier allows is a separate question from what your own portal allows. Your system can hold the booking, record what the customer has paid, and show the balance still owing against that file, so your staff always know who still needs to be chased and by when. That side of it is under your control.

The supplier side is where it gets harder. A hotel sold on a pay at hotel or a pay later rate will often let you hold the room without sending money straight away, so a deposit from your customer sits comfortably alongside it. Flights are usually the opposite. Once a ticket is issued the airline wants the whole fare, so if you have only taken a deposit you are funding the difference yourself until the customer pays the rest. Some agents get around this by holding the seats without issuing where the airline permits it, but the time you are given is short and the fare can move before you issue.

You also need to decide what happens when the balance is not paid. You can set a due date on the booking, have the system remind both the customer and your team as that date comes closer, and agree in advance whether the trip is cancelled and whether the deposit is returned or kept.

Before you offer part payment openly on your website, check with each supplier what their rates and fares allow, and make sure your booking terms tell the customer plainly when the balance falls due and what happens if it is late.