Priority and sensitivity deserve a clear rule. A customer writing in anger or mentioning a deadline should not wait in the same queue as a routine question. We agree with your support lead how the agent marks such tickets, who sees them first and how they are escalated, and we test those cases with sample conversations.
Zendesk is where many teams track support work, so the useful link is a clean ticket. When the agent cannot resolve something, it can create a ticket with the customer's details, a summary of the issue and the conversation attached. Your team picks it up with context, instead of starting from a blank subject line.
Agents amplify whatever process you already have. If tickets arrive uncategorised, the agent's tickets will be as well, so agree fields, categories and priorities early. Decide what the agent may do on its own, such as look up a ticket status, and what it should leave to staff, such as closing a ticket or promising a refund. Someone with admin access grants permissions, and we keep them to what the work needs.
Read a sample of agent-created tickets each week. Are they clear? Did the customer have to repeat anything? Are some categories flooding in because the agent failed to answer something it should have known? Those answers show whether to improve the knowledge base, the routing rules or both. Fewer repeat tickets on simple topics is a good sign, and your team can then spend more of its time on the hard ones.