Hook up between sink basket and P-trap
If the sink is deeper so that there is no longer room for the dishwasher connector, the only solution I know of is to move the P-trap† lower.

This may mean a considerable amount of cutting of wastepipes and joining new sections of pipes. If the wastpipe does not lead to an accessible vertical wastepipe, you might need to remove the back of the cupboard under the sink (or cut a large hole and re-patch later)

Some sink manufacturers sell specialized fittings that may make the problem easier to solve.

If the difference in height between old and new sink is small, you can try a flexible coupling between trap and drainpipe - here's one I used in similar circumstances - you have to reposition the trap using its swivelling connections to make room for the flexible coupling