Advice on TFT Screen and nano pinout

Good day

I’m a newby with arduino and want to design a school project with my Arduino nano. I’m looking at a project that currently uses a I2C 1602 LCD, 4 tactile switches (buttons) and 74HC595 shift register. In order to improve appearance I’m thinking of replacing the LCD and switches with a 2.4" 240x320 SPI TFT LCD with SD Card.

Before I order the new LCD I wanted to make sure that this would work given the pinouts on my Nano. (I’ve attached jpg with current pinouts. My question is if I will be able to accommodate the new LCD touch panel as well as the 74HC595 shift register at the same time given the pinouts on my Nano and if so, what pinout setup would you recommend I use?

Thank you.