The endpoint /networks/[networkId]/clients/[id_or_mac_or_ip]/events includes parameters for startingAfter and endingBefore. The documentation warns against client applications setting these parameters.
When you make a request to this API, the response includes a Link header. For example:
Link: <https://n000.meraki.com/api/v0/networks/N_1234567890/clients/abc12345/events?startingAfter=1476908909.0>; rel=first, <https://n000.meraki.com/api/v0/networks/N_1234567890/clients/abc12345/events?startingAfter=1517256994.237001>; rel=next, <https://n000.meraki.com/api/v0/networks/N_1234567890/clients/abc12345/events?endingBefore=1548874564.0>; rel=last
You can use the values of startingAfter or endingBefore in the Link header to work your way through all events for a given client.
If you want to throw caution to the wind (as I might have done), you could try adding the endingAfter parameter to your original request and including the current unix epoch.
Otherwise, the API seems to return the oldest events.