Let's just put it this way, acquiring and then operating an ACC is a huge undertaking which very few countries are able and willing to do. It seems that many here purely want to get an ACC for prestigious purposes. This is not the reason to get anything, you are incurring an inherent opputrunity cost of spending on other assets that could fit better into established doctrine. I'll expand my argument but note I will use examples from other nations including India for illustrative purposes.
Like I said before the main issue with operating an ACC is the costs and this can be broken down furth- initial costs of production/procurement, training costs, airframe/air compliment costs, maintenance costs, opeating costs, life cycle costs and CBG costs.
An ACC is inherently a large ship and these days very advanced so building or procuring one is going to cost at least 700-1BN USD if Pakistan was interested in domestic construction we could see these costs 1.5-2 times greater.
Training relatively isn't a huge expense but it is going to be considerable especially as the PN has no previous experience operating an ACC. You could expect costs of probably 50-150 million for this alone. There is also the issue of where the PN would recieve this training as I'm not sure if other ACC operating nations would either be willing or abl to train the PN for such operations. And Paksitan's freind China would be of little help here as they too have little to no experience themselves of such ops and are themselves on a path of learning through isolation.
The air wing procurement costs are naturally going to be huge. As we don't know what a/c the PN would get to operate off any future ACC let's assume it is the J-11. A decent amount of these is going to cost proboboly close to 1BN coupled with anther 500-800 mn for the rotary wing assets this is an enormous expense.
The maintenance costs for a ship like an ACC are considerable and can cost many 100s of millions thought the life of a ship and the fact that Pakistan is unlikely to be able to conduct major maintence issues in Paksitan mean the costs are even higher as the ACC will have to be sent to a foreign shipyard for such crickets to e carried out.
The operating costs of ACCs is HUGE having 1-3000 people embarked at anyone time (equal to the size of dozens of crews on smaller PN ships) presents a significant challenge in the way of costs and salaries. Addtionally the day to day costs of operating the ACC in the way of fuel and aviation fuel would be significant.
The life-cycle costs for an ACC would be significant and almost as much as the cost of the initial procurement. Having to hav the ACC undergo multiple MLUs and, as mentioned earlier, most likely in foreign shipyards would be easily 1BN USD.
A PN being as expensive as it is means that it as to go round with a potent CBG -using an IN analogy for future CBGs,this would consist of 1/2 P-15A Destroyers, 2/3 Frigates(Shvlaik or Talwar), 1/2 fleet replenishment tankers, 1/2 SSKs and 1/2 P-28A corvettes. This CBG in costing terms is about almost 6BN USD excluding the cost of the actual CBG. As such a CBG of the IN costs, all told, about 10BN USD. Of course the PN scenario is different but even still the costs to PN would be huge and it would take a huge proportion of the entire PN surface fleet just to serve the ACC. As the PN doesn't operate any destroyers there would be this gap in defences which could be deadly for any PN CBG.
Then there is the issue of doctrine. We are always told that the Pakistani military as a whole is purely defensive so inducting an ACC which is solely and offensive weapon would undermine this greatly. Addtionally the actual combat effectiveness of the PN ACC would most likely be incredibly limited. The great cost of the ACC relative to the Paksitani defence budget means it would be almost in possible to justify using it in any sort of conflict for fear of losing it and would thus also be a primary target for the IN/IAF.
All told it seems for The foreseeable future (20 years atleast) it is hard to see the PN even thinking about getting an ACC. Doing so would actually compromise the capabilities of the PN and drain the annual defence budget to such an extent most other capital spending would effectively have to cease.