I want to flag up overdue subscriptions

I want to flag up overdue subscriptions where date last paid < today’s date -365. Conditional formatting? Can I use date format dd/mm/yy?

Thge only good date format is YYYY-MM-DD as standardised under ISO 8601.

Dates are by default represented by integer numbers in spreadsheets. It’s this kind of dates that can be formatted in different ways. The respective cells answer TRUE if asked =NUMBER(myCellReference).
If you have dates represented by numbers, the currently used formats are of no meaning in any calculation or comparison.

If you entered (imported) dates in a way preventing the conversion into numbers, you can only compare for equality with dates also given as texts and in the same format.

The condition can be expressed as A1 < TODAY() - 365 where A1 is the cell containing the date last paid. This formula expression can be entered either as a formula cell (returning TRUE or FALSE) or as formula in a conditional format.