$$AgNO_3 + NaNO_3 + Ag \longrightarrow$$
Silver (Ag) undergoes a reduction process, with its oxidation state changing from +1 in \(AgNO_3\) to 0 in elemental Ag. In this transformation, it gains one electron.
There are no other elements that change their oxidation states, neither \(Na\) nor \(NO_3^-\), as they remain as \(NaNO_3\).
Therefore, in the Ag\(NO_3\) plus Na\(NO_3\) \(\longrightarrow\) Ag reaction, one electron was transferred.