As a general principle, experiment and observe. You can try different things to see how they work (I'll suggest one below). Another way to experiment is to try to do to a smaller but advanced sparring partner what this sparring partner is doing to you, and seeing how they handle it. Be aware of everything - position before the hook punch, how the block's done, whether it's better to lean into the hook to strength then block or lightly transition away using the power of the hook, and especially the footwork, counter-attack and target selection for the counter - it might be that a straight counter isn't the best choice here.
As for concrete things to experiment with... it's a bit hard to recommend something when you haven't said who's orthodox or southpaw, and what kind of block you're employing. Still - when you have an attack like a hook punch coming at you, when you block it the power of the punch will transfer through your vertical axis of rotation (which will pass through your centre of mass) somewhere: if the punch is caught out in front, then it will tend to rotate your front shoulder away from your opponent, making it hard to counter with a straight punch with the non-blocking arm. If the punch is blocked in line with your centre, your body will move linearly in the direction of the punch, which also makes it fairly hard to counter, particularly if your feet are forced to move, but if you lean slightly towards the punch then the punch may straighten you up to vertical again ready to counter. A third possibility is that the punch pushes into you behind your vertical axis of rotation / centre of mass, that means you can use the power of the punch to help the non-blocking side of your body rotate in to a strike.