tbh against the PN's SOSUS and boats (Hangor/Agosta 90B, possibly even an unannounced SWATS induction), the IN won't be trying to get near Pakistani shores. It's not worth it for them as the risk is way, way too high at that point, as not only would they deal with PN boats, but coastal AShMs and the PAF.
The bigger risk could be the IN trying to move farther west into the Arabian Sea as way to block shipments to and from Pakistan. However, a big reason why the PN opted to go for a much larger boat fleet via Chinese submarines rather than a few European ones was to extend boat coverages far enough to deal with that risk too.
Short of coastal threats and special/assymetric ops along littorals, I don't think there'll be a major IN vs. PN clash. The PN has built itself up to a point where it's too high-risk for the IN now.
If anything, it's the IN that has to worry about the PN trying to pull something, especially if the PN has any unannounced SWATS which, theoretically, could park up close to Indian shores and sink something.
There are likely some assets now in the PN that we will never hear of until they're either retired or will only hear of after they do something insane against the IN during a conflict.
The "silent service" has that name for a reason