If you look at a map of the 2024/25 Cypriot First Division you'll see that only teams in the southern half of the island are featured. As a matter of fact you can get a map of any season and this will be the case. That is because Cyprus is an island divided in two.
The history is complex and extensive but in a nutshell the southern half is culturally Greek and is a unanimously recognized country while the northern half is culturally Turkish and only recognized by Turkey. In between the two halves there's a UN buffer zone and two sovereign British military bases.
Because of this the leagues are separated as well, Cyprus has the league that is recognized by FIFA and UEFA, who's clubs participate in European competitions and national team in the Euro Cup and World Cup qualifiers. Northern Cyprus on the other hand does have a league and a national team but they are not FIFA affiliated, instead they participate in CONIFA competitions.
There was a time in the 70's and early 80's that the Northern Cyprus National Team was allowed by FIFA to participate in certain friendly matches but that is no longer the case. In 1988 Turkish club Genclerbirligi played a friendly match against Northern Cypriot club Turk Ocagi Limasol despite explicit orders by FIFA not to. As a result, the Turkish Federation was give a "warning penalty" and Genclerbirligi was banned from UEFA competitions for 4 years.
It is hard to imagine that Cypriot soccer will make a big jump in quality after a hypothetical unification but having more clubs in the league, a larger talent pool, and more money to invest wouldn't hurt.