I am not sure if PSL can be listed as an entity in stock market. But I get the idea - listing PSL for say 25% IPO to bring money from investors, which I don't see possible. To do that, first PSL has to be broken into pieces for unit (stock) valuation, then comes the governance structure. Also, PSL is part of PCB, therefore the proceed of it (profit) should go to development of PAK cricket, rather than dividend. If money is to bring in PSL, it should be through sponsorship, viewership, gate money and goody items (trade merchandises). I am not aware of how many sports tournaments (like EPL NFL, NBA, MLB, NHL ...) are listed.
BUT, what can be done (which I am sure is possible), is to list PSL Franchise in Stock Exchange. This is very common in pro sports - like MU is listed and Glazers possess about 99% of MU stocks. Similarly, Kroenke now holds about 75% of Arsenal's share, FSG holds 100% of Liverpool's share (among which, principal owner J Henry holds over 50% alone). More or less every pro sports club/franchise are listed in stock market and a major share is kept by the people we recognize as owner. Shahid Khan also is major share holder of Jaguars & Fulham. Jerry Jones owns (means hold almost 99% shares) of the richest Sports Club in world - Dallas Cowboys (valuation ~$4.5bn).
In that regard, I don't think it's upon PCB to decide if Salman Iqbal wants to list his Company (Here Karachi Kings) to be listed or not. What S Iqbal can do is list do a proper valuation of K Kings, and offer IPO to bring investment - % of IPO depends how much control he wants share with investors. That money can be reinvested in franchise for hiring players, coaching staffs, developments facilities ..... in return, KK will increase it's equity through image rights, brand value, assets (players are assets) and increase revenue from various sources (like Liverpool is trying for a mega kits deal worth 75mn BP+/year), which after netting off annual costs can be shared to investors as dividends, bonus shares or simply can be retained as company assets for future. This is very common - after J Mou's sacking MU's share price increased at NYSE
Sports tournaments, leagues are a sort of platform where thousands of investors put their money via the participant clubs and earns from clubs profit - not aware if any such League is listed.