TLDR: Don't unpublish old pages. If users land on past event pages, show them a way for them to get tickets for upcoming events.
Full story --
You are essentially dealing with three objects -- the artist, the event, and the venue. There are two ways to handle URLs for them.
Option 1. Events are treated as attributes of artists and venues pages.
http://example.com/artist/justin-bieber/ is the landing page that lists his upcoming shows. Anytime you land on this page, it will show his upcoming events if any, but never his past events.
Similarly, the venue page (http://example.com/venue/highline-ballroom-new-york/) will contain a list of upcoming events. In this option, you don't have to worry about archiving past event pages, because there are none. The artist and venue pages will always show the most recent info.
This is similar to buying, say, an iPhone. iPhone has its own page, but color, size, and memory are its properties that you select on that page. In other words, there is apple.com/iPhone/ but not apple.com/iphone-silver-16gb-verizon/
A real example: https://www.ticketmaster.com/Justin-Timberlake-tickets/artist/847841. This is the artist page that lists his concerts.
Similarly, the venue page is https://www.ticketmaster.com/Madison-Square-Garden-tickets-New-York/venue/483329.
Option 2: Events, artists, and venues, all have their own dedicated pages.
The event page is the main landing page and the artist and the venue are treated as its attributes. It seems this is your architecture.
Example: http://example.com/justin-bieber-live-in-concert-madison-sq-nyc-may-2018/. This is the event page that contains information about the artist and the venue, which are the attributes of the event page. In this situation, you will have to deal with past events' pages.
You should not delete them. Let them remain indexed in search engines. The indexed content is good for SEO. If the user lands on a past event's page, you can either:
a) redirect them to the upcoming event's page for that artist. Or,
b) display the past event's page with a big alert informing the user that this is a past event and how to get tickets for upcoming events. This design covers the use-case in which a user is looking only for information about a past event.
A real example: https://www.ticketweb.com/event/southbound-allman-brothers-tribute-shank-hall-tickets/6908535/. This is a past event page that contains info about the artist.