A freezer unit tends to use more energy while it ages. However, the embodied carbon of a new unit is always huge. 

To decide whether or not to replace an old freezer with a new, more-efficient one is not straightforward. You will need to balance the energy costs of keeping the old unit with the disposal impact and also the embodied carbon of a new unit. At the same time, keep in mind that energy sources tend to be greener over time. 

If in doubt, talk to an expert, but keep away of greenwashing!