SN74AHC14: Is it OK to connect 1K pull up resistor to 5V at the output of SN74AHC14PWR powered by 3.3V?

The clamp current is the current that flows from the I/O pin into V_CC (or, for negative voltages, from GND out of the I/O pin).

With the 1kΩ resistor, the current is limited to about 1.2 mA, which is OK.

However, the 3.3 V supply must be able to sink this current. If this is not the case, the supply voltage will float up, and all devices connected to that 3.3 V supply might be damaged.

A device with open-drain outputs would not have these problems.