As NeoPa says, what you want is quite easy, but unwise. What happens when you delete a record? There will be a break in your numbers. What happens if you have forgotten to to add a visit and the date of that visit precedes the last visit entered for that client? Then the numbers will be out of sequence with the dates.
The normal way of handling this situation is to have the main form for the client, and a continuous subform showing all the visits in date order.
If you really do insist on a visit number, have a look at something like
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DMax("VisitNo", TblVisits", "ClientID = " & ClientID) + 1
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Phil