Can I hold a flight seat for my customer while they decide, without paying for it straight away?

Yes, on some airlines you can hold a seat for a short time before paying, but it is not something every airline offers and it is never guaranteed.

Where it is available, the hold works by creating the booking in the airline's system without issuing the ticket. The seat, and usually the fare, are kept for a set period, which can be a few hours or a day or two depending on the airline and the fare you picked. Your customer gets a booking reference and can come back and pay before the deadline. If the payment does not arrive in time, the airline cancels the booking by itself and the seat goes back on sale, so your staff should always treat an unpaid hold as something that can disappear.

Whether the option shows up for a particular search comes down to the supplier behind that fare. Full service carriers are more likely to allow it than low cost ones, and cheap promotional fares are often left out even on airlines that normally permit a hold. Some suppliers also charge a fee for keeping the seat. Because of this you will see the option on some results and not on others, so it is safer to treat it as a bonus rather than something you promise every customer up front.

If holding seats matters to the way your agency sells, ask which of your connected suppliers support it and how long their deadlines run, and set a simple internal rule for chasing customers before a hold expires.