Bigger gear ratios need to have a compatible rear mech. Here’s GCN guide to choosing the right one.
If you decide you want a bigger sprocket on the back for climbing, chances are that you’ll need a longer rear derailleur that will keep the right amount of tension on the chain and clear that big sprocket. With a fairly simple bit of maths, you can determine the right size you need. GCN also go into the other considerations you need when switching gear ratios – chain length for example.