At delivery, when the client is relieved, and specifically. Naming the client type wanted, such as someone self-employed who dreads filing, produces substantially more referrals than a general request made later by email.
At delivery, and specifically. Both halves matter.
Timing. When you hand over a completed return, the client feels relief. It is the single highest-receptivity moment in the entire relationship, and it happens once a year. An email in June asking for referrals lands with someone who has not thought about taxes in months.
Specificity. "If you know anyone who needs a tax preparer, send them my way" asks the client to search a category. "Do you know anyone else who is self-employed and dreading this?" describes a specific person in a specific state, which is a question the brain can actually answer.
Practical points:
One more thing worth building: a short automated message a week after delivery, thanking them and including a review link. Reviews and referrals both compound, and neither happens without asking.
The Tax Advisor BrandPack is ready to use, fully customizable, and done for you, so you get all the marketing assets you need.