There are many ways to accomplish this, depending on factors such as the size of your venue, the functionality you need (QR code scanning, seating charts, etc.)
Ideally, the ticketing system can be integrated in a seamless way with the website content. Each event (music performance, comedy performance, theater performance, etc.) can be a web page in WordPress. Then, each page can be linked to the ticketing system to sell event tickets. Ideally, the real-time inventory status reflects back onto the web page to inform customers when an event has low inventory or is sold out.
Factors to keep in mind are:
You may have several objectives for syncing the ticketing system with WordPress. If you wish to have events pull into WordPress automatically as Posts, your ticketing system will need an API that a developer can connect to. (Some ticketing systems even offer WordPress plugins that encapsulate this functionality.) If you wish to have event inventory sync over to WordPress, your ticketing system will need an API that can overlay a status on the event and in the event calendar.
There are several approaches.
The easiest is to create a page that represents an event and link it to the ticketing system.
However, a better way is to have the ticketing system events sync with WordPress posts, and have event metadata shared between the post and the ticketing system. Ticket inventory information can be overlaid on top of an event calendar and the event page in real-time so that fans know ticket availability.
The best ticketing systems will seamlessly offer a cart that appears synchronized between the WordPress site and the venue ticketing system. While rare, this is a superior feature, and can allow customers to purchase tickets for several events simultaneously in the same cart and checkout experience.