why is chlorine have a higher ionization than sulfur?

The ionization energy of an element is defined as the enthalpy change when 1 mole of atoms of this element in gaseous state releases 1 mole of electrons to form 1 mole of singly-charged ions in gaseous state.

The equations for ionization of chlorine and sulfur are shown below :
Cl(g) → Cl⁺(aq) + e⁻ …. ΔH = ionization of of Cl
S(g) → S⁺(aq) + e⁻ …. ΔH = ionization of of S

Each of Cl and S atoms has 3 filled electronic shells. The nuclear charges of Cl and S atoms are 17 and 16 respectively.

The electrons in the outermost shell of Cl atom experiences a strong nuclear attraction than that of S atom. This is because Cl has a greater nuclear charge than S atom but they have the same number of filled electronic shells. Therefore, chlorine has a higher ionization energy (or ionization enthalpy) than sulfur.

It chlorine it contains one more electron in its valency shell compared to sulphur.

Due to the increase in effective nuclear charge on the electrons it requires more amount of energy due to decrease in size of the atom.

So, it is having greater ionisation energy than sulphur atom.

Chlorine really, really wants electrons. It's not going to give them up.