Answer
The effective nuclear charge $Z_{eff}$ experienced by the valence electrons would increase.
Work Step by Step
From left to right across a period in the periodic table, the nuclear charge of the element $(Z)$ increases. The reason is that the nucleus of the atom would have more protons, which are positive charged, so the attraction between the nucleus and the electron would be greater and greater.
Though also as we go from left to right across a period, the number of valence electrons also increases, the electrons in the same shell do not create much repulsion among each other. Therefore, the screening effect, represented by the screening constant $(S)$, remains rather stable.
So, according to the formula $$Z_{eff}=Z-S$$
Since $Z$ keeps increasing and $S$ does not change much, from left to right across a period in the periodic table the effective nuclear charge $Z_{eff}$ experienced by the valence electrons would increase.
